Quantum mechanics, as we all know, is weird. It’s weird enough in its own right, but when some determined experimenters do tricks that really bring out the weirdness in all its glory, and the results are conveyed to us by well-intentioned but occasionally murky vulgarizations in the popular press, it can seem even weirder than usual.
Last week was a classic example: the computer that could figure out the answer without actually doing a calculation! (See Uncertain Principles, Crooked Timber, 3 Quarks Daily.) The articles refer to an experiment performed by Onur Hosten and collaborators in Paul Kwiat’s group at Urbana-Champaign, involving an ingenious series of quantum-mechanical miracles. On the surface, these results seem nearly impossible to make sense of. (Indeed, Brad DeLong has nearly given up hope.) How can you get an answer without doing a calculation? Half of the problem is that imprecise language makes the experiment seem even more fantastical than it really is — the other half is that it really is quite astonishing.
Let me make a stab at explaining, perhaps not the entire exercise in quantum computation, but at least the most surprising part of the whole story — how you can detect something without actually looking at it. The substance of everything that I will say is simply a translation of the nice explanation of quantum interrogation at Kwiat’s page, with the exception that I will forgo the typically violent metaphors of blowing up bombs and killing cats in favor of a discussion of cute little puppies.
So here is our problem: a large box lies before us, and we would like to know whether there is a sleeping puppy inside. Except that, sensitive souls that we are, it’s really important that we don’t wake up the puppy. Furthermore, due to circumstances too complicated to get into right now, we only have one technique at our disposal: the ability to pass an item of food into a small flap in the box. If the food is something uninteresting to puppies, like a salad, we will get no reaction — the puppy will just keep slumbering peacefully, oblivious to the food. But if the food is something delicious (from the canine point of view), like a nice juicy steak, the aromas will awaken the puppy, which will begin to bark like mad.
It would seem that we are stuck. If we stick a salad into the box, we don’t learn anything, as from the outside we can’t tell the difference between a sleeping puppy and no puppy at all. If we stick a steak into the box, we will definitely learn whether there is a puppy in there, but only because it will wake up and start barking if it’s there, and that would break our over-sensitive hearts. Puppies need their sleep, after all.
Fortunately, we are not only very considerate, we are also excellent experimental physicists with a keen grasp of quantum mechanics. Quantum mechanics, according to the conventional interpretations that are good enough for our purposes here, says three crucial and amazing things.
- First, objects can exist in “superpositions” of the characteristics we can measure about them. For example, if we have an item of food, according to old-fashioned classical mechanics it could perhaps be “salad” or “steak.” But according to quantum mechanics, the true state of the food could be a combination, known as a wavefunction, which takes the form (food) = a(salad) + b(steak), where a and b are some numerical coefficients. That is not to say (as you might get the impression) that we are not sure whether the food is salad or steak; rather, it really is a simultaneous superposition of both possibilities.
- The second amazing thing is that we can never observe the food to be in such a superposition; whenever we (or sleeping puppies) observe the food, we always find that it appears to be either salad or steak. (Eigenstates of the food operator, for you experts.) The numerical coefficients a and b tell us the probability of measuring either alternative; the chance we will observe salad is a2, while the chance we will observe steak is b2. (Obviously, then, we must have a2 + b2 = 1, since the total probability must add up to one [at least, in a world in which the only kinds of food are salad and steak, which we are assuming for simplicity].)
- Third and finally, the act of observing the food changes its state once and for all, to be purely whatever we have observed it to be. If we look and it’s salad, the state of the food item is henceforth (food) = (salad), while if we saw that it was steak we would have (food) = (steak). That’s the “collapse of the wavefunction.”
You can read all that again, it’s okay. It contains everything important you need to know about quantum mechanics; the rest is just some equations to make it look like science.
Now let’s put it to work to find some puppies without waking them up. Imagine we have our morsel of food, and that we are able to manipulate its wavefunction; that is, we can do various operations on the state described by (food) = a(salad) + b(steak). In particular, imagine that we can rotate that wavefunction, without actually observing it. In using this language, we are thinking of the state of the food as a vector in a two-dimensional space, whose axes are labeled (salad) and (steak). The components of the vector are just (a, b). And then “rotate” just means what it sounds like: rotate that vector in its two-dimensional space. A rotation by ninety degrees, for example, turns (salad) into (steak), and (steak) into -(salad); that minus sign is really there, but doesn’t affect the probabilities, since they are given by the square of the coefficients. This operation of rotating the food vector without observing it is perfectly legitimate, since, if we didn’t know the state beforehand, we still don’t know it afterwards.
So what happens? Start with some food in the (salad) state. Stick it into the box; whether there is a puppy inside or not, no barking ensues, as puppies wouldn’t be interested in salad anyway. Now rotate the state by ninety degrees, converting it into the (steak) state. We stick it into the box again; the puppy, unfortunately, observes the steak (by smelling it, most likely) and starts barking. Okay, that didn’t do us much good.
But now imagine starting with the food in the (salad) state, and rotating it by 45 degrees instead of ninety degrees. We are then in an equal superposition, (food) = a(salad) + a(steak), with a given by one over the square root of two (about 0.71). If we were to observe it (which we won’t), there would be a 50% chance (i.e., [one over the square root of two]2) that we would see salad, and a 50% chance that we would see steak. Now stick it into the box — what happens? If there is no puppy in there, nothing happens. If there is a puppy, we have a 50% chance that the puppy thinks it’s salad and stays asleep, and a 50% chance that the puppy thinks it’s steak and starts barking. Either way, the puppy has observed the food, and collapsed the wavefunction into either purely (salad) or purely (steak). So, if we don’t hear any barking, either there’s no puppy and the state is still in a 45-degree superposition, or there is a puppy in there and the food is in the pure (salad) state.
Let’s assume that we didn’t hear any barking. Next, carefully, without observing the food ourselves, take it out of the box and rotate the state by another 45 degrees. If there were no puppy in the box, all that we’ve done is two consecutive rotations by 45 degrees, which is simply a single rotation by 90 degrees; we’ve turned a pure (salad) state into a pure (steak) state. But if there is a puppy in there, and we didn’t hear it bark, the state that emerged from the box was not a superposition, but a pure (salad) state. Our rotation therefore turns it back into the state (food) = 0.71(salad) + 0.71(steak). And now we observe it ourselves. If there were no puppy in the box, after all that manipulation we have a pure (steak) state, and we observe the food to be steak with probability one. But if there is a puppy inside, even in the case that we didn’t hear it bark, our final observation has a (0.71)2 = 0.5 chance of finding that the food is salad! So, if we happen to go through all that work and measure the food to be salad at the end of our procedure, we can be sure there is a puppy inside the box, even though we didn’t disturb it! The existence of the puppy affected the state, even though we didn’t (in this branch of the wavefunction, where the puppy didn’t start barking) actually interact with the puppy at all. That’s “non-destructive quantum measurement,” and it’s the truly amazing part of this whole story.
But it gets better. Note that, if there were a puppy in the box in the above story, there was a 50% chance that it would start barking, despite our wishes not to disturb it. Is there any way to detect the puppy, without worrying that we might wake it up? You know there is. Start with the food again in the (salad) state. Now rotate it by just one degree, rather than by 45 degrees. That leaves the food in a state (food) = 0.999(salad) + 0.017(steak). [Because cos(1 degree) = 0.999 and sin(1 degree) = 0.017, if you must know.] Stick the food into the box. The chance that the puppy smells steak and starts barking is 0.0172 = 0.0003, a tiny number indeed. Now pull the food out, and rotate the state by another 1 degree without observing it. Stick back into the box, and repeat 90 times. If there is no puppy in there, we’ve just done a rotation by 90 degrees, and the food ends up in the purely (steak) state. If there is a puppy in there, we must accept that there is some chance of waking it up — but it’s only 90*0.0003, which is less than three percent! Meanwhile, if there is a puppy in there and it doesn’t bark, when we observe the final state there is a better than 97% chance that we will measure it to be (salad) — a sure sign there is a puppy inside! Thus, we have about a 95% chance of knowing for sure that there is a puppy in there, without waking it up. It’s obvious enough that this procedure can, in principle, be improved as much as we like, by rotating the state by arbitrarily tiny intervals and sticking the food into the box a correspondingly large number of times. This is the “quantum Zeno effect,” named after a Greek philosopher who had little idea the trouble he was causing.
So, through the miracle of quantum mechanics, we can detect whether there is a puppy in the box, even though we never disturb its state. Of course there is always some probability that we do wake it up, but by being careful we can make that probability as small as we like. We’ve taken profound advantage of the most mysterious features of quantum mechanics — superposition and collapse of the wavefunction. In a real sense, quantum mechanics allows us to arrange a system in which the existence of some feature — in our case, the puppy in the box — affects the evolution of the wavefunction, even if we don’t directly access (or disturb) that feature.
Now we simply replace “there is a puppy in the box” with “the result of the desired calculation is x.” In other words, we arrange an experiment so that the final quantum state will look a certain way if the calculation has a certain answer, even if we don’t technically “do” the calculation. That’s all there is to it, really — if I may blithely pass over the heroic efforts of some extremely talented experimenters.
Quantum mechanics is the coolest thing ever invented, ever.
Update: Be sure not to miss Paul Kwiat’s clarification of some of these issues.
February 27th, 2006 at 3:58 am
[…] Update: Wait, there’s more! Sean Carroll at Cosmic Variance explains it all in terms of salad, steak, and sleeping puppies (no, really! I told you physics was beyond parody). As a bonus he tells you all you need to know about quantum mechanics, and notes that “the rest is just some equations to make it look like science.” […]
February 27th, 2006 at 4:30 am
Good Lord.
I think that actually made sense.
Careful, Sean, you might get your membership in the Kool Kwantum Kids Klub revoked
February 27th, 2006 at 4:38 am
beautiful post, sean. and that puppy clinches it.:)
February 27th, 2006 at 4:42 am
‘But there’s a catch. The outcomes of quantum processes can never be predicted precisely, but only in terms of probabilities. So quantum computation doesn’t invariably give the right answer.’ - http://www.nature.com/news/2006/060220/full/060220-10.html
A very useful, reliable step forward for computing….
February 27th, 2006 at 5:04 am
*Golf clap*
February 27th, 2006 at 5:17 am
Thanks for the applause, is it because I’ve been trying to get interest in a more reliable future computer scheme which is based on award-winning wafer scale technology? See http://www.ivorcatt.com/3ew.htm ? (Linked from my page)
February 27th, 2006 at 5:42 am
So we may now contemplate a simple desk-top calculator?, that is sitting alone waiting for an office user to interact.
The calculator is performing all kinds of calculations in anticipation of its next function!
Next time you switch on a “casio” calculator, just because a “zero” pops onto screen, do not take it for granted, internally the casio may have performed mathematical miricles in order to arrive at the default “zero”!
February 27th, 2006 at 6:49 am
I think I almost got that. I’ve bookmarked this, and promise to try again when I haven’t had three glasses of wine.
February 27th, 2006 at 6:49 am
Afterthought: Or, maybe I should try again after another two.
February 27th, 2006 at 7:04 am
OK,
So how do we get this to extremely large numbers into their prime factors. It seems like a lot of work for a single bit of information. The “promise” of quantum computing is that very large problems become accessible. It seems like this approach would lead to more “virtual calculations” to get the the answer than traditional methods.
What am I missing?
February 27th, 2006 at 7:17 am
Counterfactual Physics Blogging
OK, let’s say you want to explain something really difficult, like counterfactual computation with quantum interrogation, but you don’t want to actually sit down and do all that typing (let’s say you have a big stack of lab reports to…
February 27th, 2006 at 9:02 am
Thanks Sean. I took their paper home to read over the weekend but didn’t make much progress on it. Your precis was very helpful.
February 27th, 2006 at 9:05 am
[…] Das Thema der Quantenphysik bringt viele Menschen zur Verzweiflung. Erst kürzlich wurde berichtet, dass ein Quantencomputer das Ergebnis einer Berechnung ausgegeben hat, ohne selbige Berechnung tatsächlich durchzuführen. Das heißt, der Rechner spuckte ein Ergebnis aus, ohne in Betrieb zu sein. Jean von Cosmic Variance hat nun eine hübsche Erklärung dieses Phänomens in seinem Blog gepostet. Er verwendet als Vergleich einen kleinen Welpen in einer Kartonschachtel. Klingt auf Anhieb sehr unkonventionell, ist aber durchaus effektiv und bringt deutlich mehr Licht in dieses mysteriöse Themengebiet der aktuellen Physik. […]
February 27th, 2006 at 9:27 am
Can a salad be rotated into a cooked steak? Imagine how easy this could make food preparation: make something simple, then rotate its wavefunction to something more elaborate. But I suspect a conservation law is violated here. I guess we won’t know for sure until that grant application for the Quantum Food Sciences Institute comes through….
February 27th, 2006 at 9:39 am
Elliot, I didn’t really tackle the “quantum computation” part of the experiment, only the “quantum interrogation” part. That would be another post. But the basic philosophy is the same — you take advantage of superposition, which means that states are not simply described by bits but by functions of bits, to sneakily do many calculations at once.
February 27th, 2006 at 9:42 am
Hmm… I have bookmarked this entry for my own reference when we get to the quantum theory unit of the course. If I can do it properly, not only will my students better appreciate the weird wonderfulness of quantum theory, but they will also be hungry. The cafeteria should offer me a percentage of the take that day…
February 27th, 2006 at 10:08 am
Okay… very fine explanation!
But why doesn’t this then allow spacelike communication with entangled states? Imagine a “channel utility” midway between the two communicating sites that sends out paired entangled states to each of them. And site A does a “receipt” from site B by executing this Quantum Zeno thing and finding with high probability whether the state is pure or not without observing it. If it is we can conclude (in a perfect universe) that the collapse was due to an observation made at site B. B of course transmits a bit just by observing the state. Because A didn’t collapse the state itself, the usual popular arguments against spacelike communication through entanglement appear to fail.
BTW the channel described above is only used for communicating B to A. Communications A to B use a different channel.
February 27th, 2006 at 10:13 am
There is a fourth thing about quantum mechanics to be explained - how the quantum chef can not only prepare states of superposition of steak and salad, but also, having once prepared them, rotate them, so that e.g. salad -> -steak and steak -> salad.
February 27th, 2006 at 10:45 am
This quote is misleading. The point is that you can make the probability of getting the wrong answer as low as you want. You can make it 1^(-15) if you like, or 1^(-100) if that’s how much accuracy you need. There have been probabilistic algorithms in computer science since long before quantum computing was thought of; quantum computers just let us put additional algorithms into the general class of probabilistic algorithms with arbitrarily low probability of giving the wrong answer.
February 27th, 2006 at 10:48 am
For the lay people in the crowd, “simplified” while the “complexity” comes later in entanglement issues.
Murray Gellman called this process, “Plectics.” So under the heading of “interrogation,” I am wondering.
February 27th, 2006 at 11:19 am
Can one really make the precision of measurement arbitrarily small via the quantum Zeno effect? Assuming it takes a smaller (or larger) amount of energy to rotate the state vector as the increment decreases, don’t you either approach doing nothing to the salad/steak or pumping an infinite amount of energy into your apparatus to make the rotation? Even the former seems forbidden by uncertainty, as you can’t apply zero energy to the apparatus.
February 27th, 2006 at 11:23 am
The main problem here is that it’s well known that puppies will get excited about pretty much anything, be it steak or salad. They are permanently in waveform-collapsing mode.
February 27th, 2006 at 11:54 am
I like puppies.
February 27th, 2006 at 12:01 pm
I’m sure there’s a housetraining analogy that could be constructed involving the superposition of a puppy in a crate in the state of having to pee or not. I suppose one might use a quantum Zeno effect to never have to take the puppy out on a cold night: If you can observe it contantly, maybe it will never have to go?
February 27th, 2006 at 12:03 pm
While a state of existance may be known in a macrosense, it still applies at a microsense as well?
G -> H -> … -> SU(3) x SU(2) x U(1) -> SU(3) x U(1)
How you see then in a global perspective, having everything “inclusive” sets the stage for the standard model to be expressed? This became, complex, yet it arose from Planck Time?
February 27th, 2006 at 12:16 pm
An “onion skin” as a calorimeter, has determined particle identifications from the collisions and resulting interaction? Glast?
February 27th, 2006 at 4:14 pm
[…] Όσοι βÏίσκουν ενδιαφÎÏον στην κβαντομηχανική και τις παÏανοϊκÎÏ‚, πλήν όμως εντελώς Ï€ÏαγματικÎÏ‚ της συνÎπειες στον κόσμο των κβαντικών υπολογιστών, Ï€ÏÎπει οπωσδήποτε να διαβάσουν το ποστ του Sean Caroll (απ’το ινστιτοÏτο Kavli στο Σικάγο [*]) με τίτλο “Κβαντική ανάκÏιση“. Îα τα εξηγήσει κανείς απλοÏστεÏα ΔΕΠγίνεται. Ως μπόνους Îχει και τις βασικÎÏ‚ αÏχÎÏ‚ της κβαντομηχανικής με κουτάβια (αντί για το “Îστω μετÏήσιμο μÎγεθος Α” που συνήθως αναφÎÏεται). […]
February 27th, 2006 at 5:49 pm
‘This quote is misleading. The point is that you can make the probability of getting the wrong answer as low as you want. You can make it 1^(-15) if you like, or 1^(-100) if that’s how much accuracy you need.’ - Ben
It’s impractical, to give it accuracy you lose the size advantages of quantum-scale computing. There are good electronics ideas which are out there that get no funding. If you look back to the beginning of nuclear power (and I’m a fan of nuclear power), similar mysticism and novelty were used to sell it to the public. Today it is called propaganda. Don’t believe what you’re told! (Media question, c 1945: ‘What about radioactive waste?’ Physicist’s reply: ‘Hospitals desperately need it to treat cancer, it’s a real life-saver, and it can also be used to preserve food by killing bacteria…’)
February 27th, 2006 at 6:39 pm
Dear Sean,
Very nice exposition. Only one question–what is a measurement? Can only experimenters and puppies make them?
-Sam
February 27th, 2006 at 6:44 pm
Hey Sean, great post on counterfactual probabilities.
How about putting some “extra” factuals into the equations nad experimental setup?
How about the experimental setup as stated by you above, but make the Salad [COLD] and the Steak [HOT]!
Whilst enjoying the philosophical implications of your post, I challenge you to make the changes, and then give us the results?
It seems that the introduction of thermal values to the experiment, have a far more profound counterfactual physical miracle!
February 27th, 2006 at 7:05 pm
In “order” to clarify the 2nd law implications:
http://en.wikipedia.org/wiki/Perpetual_motion
A simple setup of outcome could be apllied to :
In an otherwise completely empty Newtonian universe, a single particle could travel for ever at constant velocity with no violation of the laws of physics — though of course no energy could be extracted from it without slowing it down. For example, [an electron can spin around a nucleus in an atom of matter indefinitely unless it or the atom is disrupted in some way.]?
The authors have a good probability of creating a condensate, wherby Electrons can be forced to remain in constant motion around an atom indefinitely?
February 27th, 2006 at 7:23 pm
I think I need to learn that trick of rotating salads by 90 degrees to turn them into steaks… (Mmmm… steak.)
For what it’s worth: In one of his papers (a research paper no less), Michael Berry mentioned that it is silly to think of apples and oranges as being in different states of quantum fruitness.
February 27th, 2006 at 7:45 pm
Dateline Midnight March 31st 2010..First quantum computer goes on sale,..Time 01:01..computer purchased by Paul Valletta with a Cheque that is postdated with the counterfactual probabilistic (date-time) algorithm.
The postdated cheque defeats all bank clearing systems that try to process it through their inferior clearing systems, the closer they get to clearing the cheque, the farther the post-dated cheque alters it date!
13:00 hrs April 1st, Quantum computer closes all its windows and doors, shuts down and refuses to compute in any way unless it is switched off..continues to listen to an abstract track by Paul Simon, that has the catchy line..You Can Call Me Hal?…
February 27th, 2006 at 9:29 pm
Then there are my dogs, which would eat salad or steak just as readily, rendering the entire experiment moot….
February 27th, 2006 at 10:18 pm
So, someone please correct me if I am wrong here, but the “trick” is using a separate serial qubit operation to inspect the result state of a “standard” register in a quantum computer?
February 27th, 2006 at 11:09 pm
[…] If you are a physics student, or a non-physicist who happens to be simply curious about quantum mechanics, you should read Quantum Puppies by Sean Carroll over at Cosmic Variance. Well, OK, the title is really “Quantum interrogation”, but it’s cleverly done with a friendly, non-lethal puppy analogy, rather than the dead cat in the box analogy. It’s also very well written. […]
February 27th, 2006 at 11:15 pm
It makes my brain hurt just thinking about
Perhaps you have read about the researchers at the U of Illinois/Urbana-Champaign who have developed a quantum computer that can perform an operation even when it is turned off. The computer takes advantage of a peculiarity of quantum states, so that …
February 28th, 2006 at 12:04 am
Is it a given, that if a Quantum Computer can give answers to a sum without going through the calculation process, equals, the parallel to a Quantum Computer giving an answer to a question that has not been proposed?
You do not need a Quantum Computer for this surely, Microsoft have cornered this market with XP!
February 28th, 2006 at 1:09 am
I think cooper hits the nail on the head. This works because you get the puppy to do an observation instead of you, but someone is still doing an observation. Actually, that seems to be the point: if there’s a puppy, the wavefunction gets remixed whether or not the puppy makes a ruckus, whereas the wavefunction is the same if there is no puppy. Pretty slick.
February 28th, 2006 at 1:23 am
Recent Quantum Computing Advance, Brilliantly Explained
Robin posted this and then this a couple of days ago about a puzzling advance in quantum computing. Both posts confused most people who read them (even the writers at Nature seemed quite unsure of what exactly they were reporting,
February 28th, 2006 at 3:16 am
Sean: “Quantum mechanics, according to the conventional interpretations that are good enough for our purposes here, says three crucial and amazing things.”
Not good enough, since these interpretations are at the root of much ‘quantum confusion’.
Sean: “First, objects can exist in “superpositions” of the characteristics we can measure about them.”
QM assigns probabilities to possible measurement outcomes on the basis of actual measurement outcomes. That’s all there is to it - unfortunately, because this leaves so much open to debate and speculation.
Sean: “According to quantum mechanics, the true state of the food could be a combination … a(salad) + b(steak), where a and b are some numerical coefficients. That is not to say (as you might get the impression) that we are not sure whether the food is salad or steak; rather, it really is a simultaneous superposition of both possibilities.”
All that QM tells us is that if we make the appropriate measurement, we will find salad with probability A and steak with probability B. (A and B are the squares of the respective absolute values of a and b.) This is definitely not the same as saying that the food “really is a simultaneous superposition of both possibilities”.
Sean: “The second amazing thing is that we can never observe the food to be in such a superposition; whenever we observe the food, we always find that it appears to be either salad or steak.”
There is nothing amazing about it if you keep in mind what I just said.
Sean: “Third and finally, the act of observing the food changes its state once and for all, to be purely whatever we have observed it to be.”
As said (but it cannot be repeated to often), the quantum formalism is an algorithm for assigning probabilities to possible measurement outcomes on the basis of actual measurement outcomes. This algorithm (be it in the form of a density operator, a so-called state vector, or a so-called wave function) tells us nothing whatever about the objective, actual, physical (or whatever) state of the food between measurements.
Sean: “If we look and it’s salad, the state of the food item is henceforth (food) = (salad), while if we saw that it was steak we would have (food) = (steak). That’s the ‘collapse of the wavefunction’.”
Before the measurement the probabilities A and B are both greater than 0 (and thus less than 1). After the measurement either A=1 and B=0 or A=0 and B=1. Why should that be amazing, given that QM assigns probability on the basis of measurement outcomes? A new measurement outcome means new probabilities.
Sean: “You can read all that again, it’s okay. It contains everything important you need to know about quantum mechanics.”
There really is sooo much more. Take (for instance) a look at ThisQuantumWorld.com.
February 28th, 2006 at 4:47 am
What I always liked about the way the bomb problem was set up was that it was more of an actual experiment that you could do, if you were good enough — isolate the bombs from any light, make a detector that’s responsive to a single photon, that kind of thing. And that led to experiments that were actually done, like the one at LANL. In your example, it’s not clear how you’d set up interference between the salad and steak states, so it seems like it’s just some kind of analogy.
Not to complain too much, I’m all for non-violent, puppy-based experiments. But I don’t think it makes it clear that the effect is real and tested (to some degree), not some physicist’s dream.
February 28th, 2006 at 6:08 am
In a real sense, quantum mechanics allows us to arrange a system in which the existence of some feature — in our case, the puppy in the box — affects the evolution of the wavefunction, even if we don’t directly access (or disturb) that feature.
What’s the ontology that supports this?
February 28th, 2006 at 10:27 am
The question of whether the waves are something “real” or a function to describe and predict phenomena in a convenient way is a matter of taste. I personally like to regard a probability wave, even in 3N - dimensional
space, as a real thing, certainly as more than a tool for mathematical calculations … Quite generally, how could we rely on probability predictions if by this notion we do not refer to something real and
objective? [Max Born, Dover publ., 1964, “Natural Philosophy of Cause and Chance”, p. 107.]
This is the general ontological (epiontic, according to Zurek) problem. But there are specific ontologies (Bohm-de Broglie pilot waves, advanced-retarded actions, time symmetrical two-state formalism, etc.).
February 28th, 2006 at 10:30 am
[…] Cosmic Variance has a lovely explanation of how the quantum interrogation aspect of counterfactual computation might work. So I’ve moved on from last week. […]
February 28th, 2006 at 10:38 am
Gyan asks: What’s the ontology that supports this?
We ain’t got no ontology. We don’t need no ontology. I don’t have to show you any stinking ontology!
February 28th, 2006 at 12:30 pm
This whole thread is brilliant, but I particularly liked the ontology post!
T
February 28th, 2006 at 2:27 pm
Ulrich,
Your objections seem to be largely philosophical and/or semantic in nature. Do you have any objections to the conclusions?
February 28th, 2006 at 2:42 pm
The more serious question remains, if the puppy is consumed without having been cooked, how can you be sure it was skinned?
February 28th, 2006 at 3:14 pm
Controlling temperature might be very important?
February 28th, 2006 at 4:22 pm
agm:
Thanks.
Ok — and please forgive me as I am certainly no trained physicist — but it seems to me what this really is, for lack of a better description, is a RAM bus for a quantum computer. I could perform (x) iterations of the same operation on a dataset, in effect “save” the current waveform state on the register out to a separate set of data (”RAM”), then use the result register to perform another set of answer-space reductions with another algorithm, collapse the system at the end, and determine the intermedia values after the fact.
Again, please let me know if I am completely off base with my understanding of this.
February 28th, 2006 at 4:55 pm
I have one question. Granted that this is a thought experiment, how is it that the non-detection of the salad by the puppy counts as a wave-collapsing ‘observation’ for the purposes of quantum mechanics? After all, the puppy can just as easily not detect the salad when the (food) is outside of the box, implying that the quantum waveform would collapse before you could put the (food) into the box, which doesn’t make sense.
February 28th, 2006 at 5:05 pm
[…] something to read when you’ve got time: Quantum interrogation | Cosmic Variance […]
February 28th, 2006 at 5:44 pm
Wouldn’t it be easier just to use a cat. I thought it was traditional to use a cat for physics analogies!
February 28th, 2006 at 6:00 pm
I’m not a physiicst… so bear with me. An issue that is puzzling me. The argument is based on the pre-supposition that you can start the food (salad) state and can then rotate the wavefunction to any intermediate state. Aren’t you collapsing the wavefunction when you start with food(salad)?
To my mind, in a non-determinate state, food = a(salad) + b(teak), where a = b. Also, how do you rotate the wave-function partially. Any observation will collapse it by rotatiing by 45 degrees. How do you bias the wavefunction without collapsing it?
February 28th, 2006 at 6:03 pm
[…] Ahh, teenagers. It reminds me of my school years. Perhaps she needs a project. I’m thinking we’ll try to turn a salad into a steak to see if it wakes Daphne up. Of course, greyhounds sometimes enjoy a good salad. […]
February 28th, 2006 at 7:23 pm
How can you put a puppy in a box, without anybody knowing it’s in there? for this to work, would’nt you need a perfect horizon, with no information leaking out, no matter how small or in which direction through time. Even if you built a machine to put the puppy in the box, you would still know what the machine was for and how can you build a machine without someone knowing what it’s for. If Alice falls down a rabbit hole, she ether leaves a teddy bear at the entrance or does not leave a teddy bear( A teddy bear is a small amount of information about what went down the rabbit hole, which is left for all to see, there is a chance you already know the answer anyhow.) If there is no teddy bear, then the possibility of alice being down the rabbit hole is Irrelavant, it just a rabbit hole..
February 28th, 2006 at 8:02 pm
Scott #52: Under the colorful assumptions of this story, the sleeping puppy is measuring the food-value of the thing we stick in the box. In particular, even if it’s salad, the puppy has measured it to be salad. A little poetic license there, perhaps.
Dibyendu #55: We are definitely assuming that the food starts in a pure-salad state. That’s okay, we can look at the wavefunction and manipulate it in the course of preparing our apparatus. What we can’t do is measure the food-value until the very end. But, as mentioned in the post, rotating the wavefunction doesn’t count as a “measurement,” since we don’t know the value of the wavefunction after we’re finished. It could be anything, depending on where it started.
February 28th, 2006 at 8:32 pm
[…] 关于这篇Nature论文的详细讨论，å¯ä»¥å‚考这篇日志。 […]
February 28th, 2006 at 8:39 pm
Enjoyed the post. Thanks.
February 28th, 2006 at 9:00 pm
[…] The quantum puppies post below was written in response to some excitement generated by recent work from Paul Kwiat’s group at UIUC; specifically, this paper in Nature (that is sadly only available to subscribers). Paul was nice enough to write a little clarification about what they actually did, which we’re reproducing here as a guest post. Hi, […]
February 28th, 2006 at 11:23 pm
[…] An nice explanation of Quantum Mechanics and its quirks. Gave me a headache at the end though — I guess I’m just dumb in figuring it out.
§ […]
February 28th, 2006 at 11:24 pm
Ulrich’s objection does not seem to be merely semantical, but rather cuts to the heart of one problem with the explanation. If the food is not “really” in both states at once, but merely has a probability of being salad or steak, that would seem to affect our ability to rotate the eigenvector. Just because the food is in an unknown state (but with known probabilities) does not, by itself, mean that we can freely change it to any other unknown state (with known probabilities). (And worse yet, as Dibyendu pointed out, the experiment requires the food to be in a non-superposition to begin with: it has to already be salad. If we adjust our apparatus as Sean suggested, that itself is a measurement, even if we don’t actually directly measure the individual salad particles that we conduct the actual experiment with: if the state is known by any means whatsoever, the state is known. This would seem to further impair our ability to rotate its state.)
That leads to a fundamental problem with quantum computing: if one assumes the ability to alter the state of quantum particles, no matter what state they’re in to begin with, then logically one could turn (say) neutrons into protons (by changing one down quark into an up quark, thus changing the neutron’s down+down+up into a proton’s down+up+up), and thus turn (say) lead into gold (albeit neutron-deficient gold, which would need more neutrons quickly to avoid fissioning…or maybe that’d be the point, and one could use this to turn ordinary matter into quickly decaying fuel for a nuclear reactor: say, turn nitrogen-14 w/7 neutrons - harvested from the air - into silicon-14 w/0 neutrons, and watch it fly apart in a cloud of energized protons - easy to capture for power production). But this possibility - a direct logical consequence of this unrestricted state alteration - appears to fly in the face of known physics, therefore this state alteration appears impossible (at least, without restrictions that would invalidate the puppy experiment analogy as it is currently written).
There’s also a problem with the fact that the puppy (if present) is performing an observation, although this may be more a problem with the analogy than with the core concept. In reality, the “puppy” would usually not be somethng ordinarily capable of performing a measurement in the same sense as we do, so the “puppy” couldn’t collapse the wavefunction (and thus presumably stop any further eigenvector rotation) on its very first measurement.
February 28th, 2006 at 11:29 pm
OK, how does one rotate the state of unobserved food? How would you put it in the box?
Does it become “observed” if a robot puts it in the box? Does moving it to the flap rotate anything?
How would you confirm that you have rotated the state, and can that be done without observing the food?
February 28th, 2006 at 11:53 pm
Update: I read the article, and…sure enough, although they did do some interesting experiments with one “rotation” (actually, the “food” is polarized photons, and what’s being rotated is apparently the polarization - from horizontal to vertical and back - not actually the probability in and of itself, although it affects other things in the system) and measurement, the Zeno chain is still just a thought experiment.
March 1st, 2006 at 3:11 am
This reminds of the puzzle where you come to a fork in the road, and there are two guys one who always lies, and one who always tells the true. They both know where the roads lead, and you want to know which is the right path, say to Town. Trick is you can only ask ONE question to one of the persons. What question could you ask? one answer is: “If I were to ask you, if this is the corrent path to town, would you say yes?” You get the right answer is all cases.
March 1st, 2006 at 3:18 am
I mostly get it, but I think he might be wrong by stating that the probability could be improved as much as you like…might the accuracy depend on the cost of the calculation? For example, if trying to factor a very large prime, you might just be trading one set of problems for another…if trying to improve the probability of your result turns out to be as computational expensive as a more straightforward (brute force) approach.
March 1st, 2006 at 3:19 am
>>OK, how does one rotate the state of unobserved food? How would you put it in the box?
>>Does it become “observed” if a robot puts it in the box? Does moving it to the flap rotate anything?
>>How would you confirm that you have rotated the state, and can that be done without observing the food?
It’s just a metaphor. Maybe this will help you understand the basic concepts:
http://video.google.com/videoplay?docid=-4237751840526284618&q=quantum
March 1st, 2006 at 3:48 am
[…] A couple of interesting science links are doing the rounds today. The first relates to Quantum Interrogation. It is worthy of special note because it is one of the few posts relating to Quantum Mechanics that mere mortals like myself have a flying chance of understanding without first doing four years of undergraduate physics. Oh, and it uses a sleeping puppy in its descriptive analogy rather than a potentially dead cat, so it is family friendly. Link found via OneGoodMove. […]
March 2nd, 2006 at 2:07 am
[…] You’ve probably heard about the quantum computer you don’t even have to turn on. And you may have heard something about quantum puppies in the discussion. Drop everything and go read Sean’s article in Cosmic Variance, and you’ll actually understand it! […]
March 2nd, 2006 at 4:17 am
[…] http://blogs.discovermagazine.com/cosmicvariance/2006/02/27/quantum-interrogation/ […]
March 2nd, 2006 at 11:19 am
Thinking is hard work
Whew! First, from 3 Quarks, there was this, and then this, and then I asked (only half-joking) if they were joking, and Abbas Raza promised a plain-language explanation — and kept his promise. So now there is this, from Cosmic Variance. I have read it…
March 3rd, 2006 at 3:33 am
48. Rob G on Feb 28th, 2006 at 2:27 pm
Ulrich, Your objections seem to be largely philosophical and/or semantic in nature. Do you have any objections to the conclusions?
Which conclusions exactly?
I agree, physics is partly maths and partly philosophy/semantics. You need the latter to figure out how the maths relates to the world. You don’t need it if you want to earn your living doing physics. The result: lousy semantics, pseudoproblems, gratuitous solutions.
I also have a comment on Adrian’s comment (63.) but need some time to formulate it.
March 3rd, 2006 at 8:06 am
63. Adrian on Feb 28th, 2006 at 11:24 pm
Just because the food is in an unknown state (but with known probabilities) does not, by itself, mean that we can freely change it to any other unknown state (with known probabilities).
Hello Adrian,
An unknown state with known probabilities is a contradiction in terms. A quantum state isn’t a classical state (a collection of possessed properties). It’s an algorithm that is used to calculate the probabilities of the possible outcomes of measurements. If we know the state, then we know the probabilities, and if we don’t know it, then we don’t know them. (Those who believe that quantum states are “states of knowledge” would consider even the notion of an unknown quantum state a contradiction in terms.)
65. Adrian on Feb 28th, 2006 at 11:53 pm
actually, the “food” is polarized photons, and what’s being rotated is apparently the polarization - from horizontal to vertical and back - not actually the probability in and of itself…
Obviously one can’t rotate probabilities! What one knows how to rotate in this particular contex is an algorithm, inasmuch as this can be thought of as a one dimensional mathematical construct (a so-called “ray”) that can be rotated in a more than one-dimensional mathematical construct (a so-called Hilbert space). But this algorithm is what determines the probabilities of the possible outcomes of all possible measurements.
the Zeno chain is still just a thought experiment.
One would think it was exciting news if what was once a thought experiment came out different than predicted. Strangely, it is exciting news every time what was once a thought experiment comes out exactly as predicted. (By the way, various more or less equivalent experiments have actually been done.)
March 3rd, 2006 at 8:42 pm
Sean, thanks for presentin QM in an understandable, albeit oversimplied manner for us old duffers and carpenters. If more physicists still spoke English then I suppose more people would pick up on it. I understand now, why you were not tenured at the UofC, since students showing up for your class would naturally stay for the rest, which defeats the economic goals of the University, and of course other Profs who would rather spend time picking their noses at the alter of ego.
March 4th, 2006 at 5:39 pm
I feel like I have been transported back into my quantum classes of college. Thanks for making those neurons fire again! Meanwhile, I am now expecting to need to assume a spherical cow for some sort of calculation.
March 6th, 2006 at 5:14 pm
I think you meant “Quantum mechanics is very very very very nearly the coolest thing ever invented, ever.”
Kevin
March 8th, 2006 at 5:37 pm
Quantum mechanics, looks to me like an information theory. A quantum computer sounds like how you would imagine a blackhole to work, you think there is twice as much information in there, but when you look, half of it seems to be missing. It not really missing tho, is it? It just that! Information, if it was space-time would be traveling through it self. The information would be curved back and traveling away from us, we cant see it because it’s wave function is rotated(we dont see information through time we just remember what we see through space. If both wave functions are rotated into a superpostion then you are looking at whatever it was, you rememberd last). Seeing stars through time, 13 billon years ago? I don’t think so… your seeing them 13 billion years through space. No information as ever travel tho time. Time would be created by rotated information, through the surface of an un-observed space. Blackholes would not stop time but create the illusion of it.
March 8th, 2006 at 6:57 pm
I wonder if this is why Preskill went to quantum computation, is to learn to write the language of ingoing/outgoing state, on what existed “on” the horizon?
March 13th, 2006 at 9:05 am
Nice! I have little knowhow on the matter so please bear with me. One objection I didn’t find in the comments is this (it’s answer is probably simple, but I don’t get it):
At one degree rotation from salad, probability of food being considered steak is low. Ok. But how does 90 one-degree rotations add upp to 90*[that low number]; why does not probability of steak increase as we approach the (90-degree) opposite of salad? At 45 degrees, for example, have not food “arrived at” equal superposition?
It seems to me as if probability of waking pup would be very high indeed after repeatadly letting it sniff high-probability steak.
Where do I go wrong?
March 14th, 2006 at 5:09 pm
Not so crazy after all…
[URL=http://www.newscientistspace.com/article/dn8836-black-holes-the-ultimate-quantum-computers.html]black holes the ultimate quantum computers[/URL]
http://www.newscientistspace.com/article/dn8836-black-holes-the-ultimate-quantum-computers.html
March 14th, 2006 at 5:39 pm
so after reading the article… When using someone else’s blackhole! Don’t forget to squirt a little bit of duck around the rim, when you’ve finished. Kills 99.9% of all information, stops spacetime echos and leaves it clean and fresh for the next object to pass through.
Don’t know what am talking about! Have a think about it next time you use someone else’s toilet.
March 14th, 2006 at 10:40 pm
I wonder, from a layman point of view.
If certain models were used (D brane thinking maybe, I dunno?), it would have had to have been with understanding certain conditions were being meet?
“Abstractness” still needed to bring comprehension of nature’s ways into the realization of the blackhole states?
Would this have raised insight into the “new physics?”
Like maybe “encouraging ideas” about “swimming in honey” or “molasse’s special brand,” as a viscosity statement, and as a way seeing dimensions and energy, travelling with infinite probability like holes, through high energy conditions?
That’s the point, the model had to have been already accomplished in that unification?
Gulp:)
March 15th, 2006 at 12:41 am
Lets take this up another gear?
Seth Lloyd:Now, Seth Lloyd of the Massachusetts Institute of Technology in the US, has used a controversial quantum model called final-state projection to try to solve the paradox. The model holds that under certain extreme circumstances — such as the intense gravitational field of a black hole, objects that would ordinarily have several options for their behaviour have only one. For example, a black hole could cause a coin thrown into it to always come up “heads”.
What this equates to is the Blackhole being a “CONVERSION” location? instance if the Blackhole imposes 100% final state into the coin being “always-heads”, then to gain this knowledge outside of the Blackhole, you must assert that, external to a blackhole, when one tosses a coin it should always turn up TAILS!..if one is dealing with an entangled coin that is.
Problem is that for any coin (say a dollar) that has passed through a blackhole horizon, when it emerges, it loses half its energy(one can assert that the coin no longer has energy of “two” sides, heads or tails, its either heads or either tails). The reduced state function imposed onto any entity that has trancended a blackhole horizon, may confine its state 100%, thereby trapping the knowledge of the dollar’s “toss” function, but does not eradicate the fact that the dollar thrown in, may emerge as a “silver-dollar”, with ist re-configured “two-state-toss” function?
In other words “Quantum -BH- Process” alows 1 dollar bits to be the input, and silver dollars 2-BITS? to be the “GAINED” output.
I believe the information “gain” is a sublte insight on the process of initial and final state paradox?
Just think about the ordinary probability of the coin-toss?..when it comes down heads, you also know it did not come down as tails?..prior to tossing of a coin you have 50% of either, after the event you have “gained” extra knowledge, you have 100% knowldedge..cause and effect?..gaining the knowledge before the coin-toss occurs, one has to subscribe to the ‘Time’ re-configuration initial state principle.
Quantum Mechanics uses the re-normalization process “after” events, Relativity by its status in Space within time, always defeats QM by its processess by default.
March 15th, 2006 at 9:33 am
Mind you this is from 2001
Our new picture is that the 3-D world is embedded in extra dimensions,” says Savas Dimopoulos of Stanford University. “This gives us a totally new perspective for addressing theoretical and experimental problems.
So how would you explain “increased” bulk manifestation?
March 15th, 2006 at 4:49 pm
I believe the gravitational tidal effects, of a blackhole would prevent, the other side of the coin, that’s falling into the blackhole from being observed? The outgoing information, would always be pushed beyond your horizon, it would fall towards its creation, with the chance of it becoming a silver coin almost nil. A bit of the information of coin that’s falling in, would always remain above the horizon, until the universe came to an end. This, then would mean, the coin will have flipped and then will, slowly become real, for the coin to become real, will take a hell of a lot of evolution (which will have already happened?). The tail side of the coin will then remain beyond the horizon, until you throw in your coin, with the one only chance, of it landing heads up. To flip the coin fast enough to have knowledge of both side, would be at great risk, of a release of an enormous amount of energy. This release could be slowed down, but would eventually cause all Quantum computers to crash, with no chance of recovery.
It may be better, to put back laws of physics 100 years or start again. Better to do it now, instead of when the sun is just about to go out. Better put them back 100 years now, rather than 6,000,000,000 years later on…
Don’t build a vessel and call it unsinkable.
April 19th, 2006 at 4:36 pm
I’ll have a wedge of lettuce with blue cheese dressing, and I like my fillet medium rare please. Do you have any A-1? Oh, on second thought, forget that. I don’t want to insult the chef.
April 27th, 2006 at 12:57 pm
[…] Feel free to stick around, though I warn you that most of our blog’s content is us going on about our kid and how cute he is except when he’s being annoying. There’s not much other science content here. Although I am a Ph.D. physicist, so there’s no telling when I’ll bust out with a comment about an explanation of counterfactual quantum computation that uses puppies to make its point. […]
April 27th, 2006 at 1:03 pm
Addressing Tullmejs question, I had the same reaction when I first read through it. But, if there is no puppy, you just do 90 consecutive 1 degree rotations and observe steak. If there is a puppy, each of the 90 times you stick the food in the box, it observes and changes the state back to a pure food state (most likely salad). Each time, there is just a 0.0003 chance that the puppy will observe steak and therefore wake up and bark. It all hinges on the fact that the puppy changes the state and you don’t observe (and therefore change the state) between each rotation. So, the three possible outcomes after 90 rotations: you observe salad - puppy exists, you observe steak and no bark - puppy doesn’t exist, you observe steak and hear a bark - puppy exists.
April 30th, 2006 at 7:02 pm
[…] I put this up elsewhere, but I like it so much that it deserves a spot here. We’ve talked about quantum computation a few times before, but how much do we really know? Metafilter, instruct thyself. Don’t forget to learn some advanced probability and computational complexity (Scott Aaronson has more). Whoa, that’s a lot o’ learning, so let’s so check out the much easier, and much cooler “sleeping puppy” experiment. I can only dream that will help break quantum mechanics’ association with animal abuse. Then, there’s the Free Will Theorem that just came out (some discussion on it) and another paper with a new look at an old problem. The latter describes another way of solving ye olde, super importanto Einstein-Podolsky-Rosen paradox using the relational interpretation of quantum mechanics (lots of discussion running around). Whew. We don’t need the crackpot ramblings of What the #$*! Do We Know? when we’ve got real physics to keep us up at night. So, who wants to become a physicist? (t’Hooft has some thoughts for those who want to go theoretical.) […]
August 17th, 2006 at 10:16 am
Programming the Universe
Programming the Universe: A Quantum Computer Scientist Takes On the Cosmos reads aloud surprisingly well. At least Eamon and I thought so, though perhaps the other vacationers didn’t appreciate it as much. I do my part to provide propoganda…
December 31st, 2006 at 2:17 pm
[…] Quantum Interrogation […]
January 18th, 2007 at 10:57 am
[…] In the shortest turnaround time for a book ever, Bora “coturnix” Zivovic (of Blog Around the Clock fame) has put together The Open Laboratory, a collection of the greatest science blogging of all time. Which is a little bit less impressive than it sounds, since science blogging hasn’t been around for that many centuries. Still, it’s a fun concept, to take all of those words on the internet and bind them between covers. I’ll admit that I nominated my own quantum puppies post, in the tradition of all great media shamelessness. […]
July 8th, 2008 at 6:26 pm
[…] about quantum mechanics. Start with the basics, try to explain this crazy theory and some of its outlandish consequences in ways that anyone can understand, and then dig into some of the mysteries of measurement, […]
August 9th, 2008 at 11:06 am
[…] in terms that should be accessible to non-experts. (One user-friendly answer to that question is here.) Happily, that didn’t take up the whole dialogue, and we had the chance to home in on the […]