Comments on: Econophysicobabble

By: Jack

Jack — Sun, 24 Oct 2004 19:06:23 +0000

In the example presented information is being transmitted. Just by cooperation I can control the awarding or not of the prize with 75% accuracy. By switching thd dial on an entangled electron spin detector I can improve the accuracy to 85%. That difference is information. In a single trial it would be hard to identify but over repeated examples I would be able to improve the bit rate for a given accuracy. This is action at a distance which is not expected to be possible but is also a famous physics problem the ins and outs of which are not discussed here. I’m surprised that this is interesting from a game theory point of view. The problem may be that although the game presented is probably the simplest for which something interesting could happen it serves as a kind of Monty Hall problem obscuring the information transition. How do you have intuitions about a piece of information smaller than a bit?

By: Eli

Eli — Sun, 24 Oct 2004 04:05:42 +0000

Once people get it settled that entanglement can’t transmit information (in the Shannon sense), it sure looks like this all comes down to disagreeing whether “no communication” means “no transmission of information” or “no interaction whatsoever”. Classically, there would be no difference, but in fact there is. We’re assuming the players are allowed to coordinate their strategy. If they can do that in person, it’s natural also to allow them to prepare an entangled pair at that time. If they’re only allowed to do their strategizing over a purely classical channel, they’re more limited. I think the point is that you might want to pay attention to that kind of distinction when defining the rules of a game. (Disclaimer: I only glanced at the paper itself.)

By: neil

neil — Sun, 24 Oct 2004 03:13:38 +0000

A question to the game theorists: In what sense are two players not ‘communicating’ if they have devices to which they can provide input which they assume goes to the other player, or can receive output which they assume comes from the other player? It seems like this pokes holes only in the definition of information flow in a physical system. Because physically, I can accept that there is no connection between the entangled particles; but I can’t accept that there is no way to transmit information over this channel. If the physics says there is, then we must have the definition of ‘transmit’ or ‘information’ wrong. The more I think about it, the more it sounds like DD’s ‘calling my wife at 5pm’ analogy is the best one here. By not calling his wife, DD has sent no signal to his wife’s telephone device, but by monitoring the device she can nonetheless determine some information about his state. There are lots of ways that the ramifications of quantum theory could affect everyday life, but this one is a big stretch.

By: abb1

abb1 — Sat, 23 Oct 2004 21:05:20 +0000

Sounds like Reimer got it exactly right: the two particles together constitute a device. Like a pair of those miraculous glasses or a phone line or a notepad with pencil or a talking God. Same idea, different mechanics.

By: junius ponds

junius ponds — Sat, 23 Oct 2004 20:44:58 +0000

To people who think a causal influence (information transfer) is involved: since the statistics of measurements are unaffected, obviously you impute some physical reality to the wave function. I’m inclined to view it as a bookkeeping device, wholly belonging to the quantum formalism, but then again, I have a strong positivist streak—but so does the Copenhagen Interpretation. I have a feeling we’re never going to feel completely satisfied so long as we keep talking about collapse and so forth.

By: junius ponds

junius ponds — Sat, 23 Oct 2004 20:36:23 +0000

>Alice can be predicted by Bob with perfect certainty< That is, without disturbing Alice’s system, due to the locality assumption. Sorry, I should have made that more clear.

By: junius ponds

junius ponds — Sat, 23 Oct 2004 20:29:28 +0000

To wit: >Junius, there is only one box, and both parties have access to it; or, alternatively, two boxes whose behavior is interdependent. Just as with Steven’s setup where you have essentially two small “quantum machines” whose behavior is interdependent.< A classical box that behaved in this manner would be impermissible because it would require propagation of signals at speeds less than or equal to c. EPR pairs exhibit the correlation without signaling.

By: junius ponds

junius ponds — Sat, 23 Oct 2004 20:25:52 +0000

I read EPR last year. EPR argue that quantum mechanics is incomplete because properties corresponding to noncommuting observables as measured by Alice can be predicted by Bob with perfect certainty, making both “elements of reality” according to a criterion they lay out. The buried assumption is locality. A hidden variables theory, as Einstein would have it, would have two canonically conjugate variables both determinate… Bohm pulled off a nonlocal hidden variables interpretation. Nonlocality is what is really important here.

By: Chad Orzel

Chad Orzel — Sat, 23 Oct 2004 20:07:49 +0000

Let me try an example that I think will speak to the confusion of several people who are posting here: You and I sit in separate rooms. Once per minute, we each receive a red or green tennis ball through our mailslots. {etc.} I haven’t read the original paper in detail, so it entirely possible that there’s some subtlety in the physics of the situation that this second example misses. If the tennis ball thing is a good analogue for what’s happening, though, I would be inclined to say that there’s nothing inherently quantum about this whole thing. The really important feature, from a quantum standpoint, of the EPR experiment, is that the state of the particles is indeterminate until one is measured. If all you care about is that there’s a particular correlation between the two particles, then it’s just a convoluted dodge around the rules of the game, and might just as well be done by exchanging classical tennis balls, or looking at a particular part of the sky at the time of the question (as somebody upthread suggested). I suspect that the physics has gotten mangled somewhere in the journey from one scenario to the other. I’m already feeling faintly ashamed of myself for wasting this much time on such a silly argument, though, so I’m probably not going to try to track down the mistake.

By: zaoem

zaoem — Sat, 23 Oct 2004 19:43:12 +0000

From Steven Landsburg’s example: “All we have to do is agree to leave off the sunglasses when we’re asked about cats, put them on when we’re asked about dogs, answer yes when we see a red ball, and answer no when we see a green.” Surely this type of agreement follows from cheap talk. I am still kind of puzzled by the relevance of all this. It strikes me that the notion that quantum theory “solves” coordination dilemmas is rather obvious in that it essentially captures an assumption about connectedness between actors, as do more common solution concepts to coordination dilemmas that focus on norms. Can we really separate quantum game theory from those more common assumptions that actors have a set of shared assumptions about their connectedness (“appropriate behavior”)?

By: Steve Carr

Steve Carr — Sat, 23 Oct 2004 15:59:25 +0000

I’m sure someone’s already made this point and I missed it in the 114 previous posts, but in Landsburg’s revised example, he writes: “When we look at them, they’re always opposite colors. We know this, for example, because we each write down the sequence of colors we see and compare them afterward.” Surely even Landsburg would have to agree that comparing sequences of colors counts as “communication” and an exchange of information. And without that communication, there’s no way to win the game (not consistently), because the people wouldn’t know that they’re seeing opposite colors.

By: Reimer Behrends

Reimer Behrends — Sat, 23 Oct 2004 14:06:37 +0000

Junius, there is only one box, and both parties have access to it; or, alternatively, two boxes whose behavior is interdependent. Just as with Steven’s setup where you have essentially two small “quantum machines” whose behavior is interdependent. Glenn, it will take a fraction of a microsecond to come up with the answer. It’s a box with a switch at each end, each with two positions labelled cat and dog (you can use a pair of computers connected by a network, with one of them running the necessary code and the other one serving as a dumb client to implement it). Whenever one participant flips a switch it will alter the output for that participant to make sure that the game is won. It’s a simple little state machine whose implementation I might give as a programming task for first year computer science students. If you want to mirror the original experiment precisely, introduce a middle position for the switch and don’t show anything for either party until they’ve moved their switch into either the cat or dog position. What seems to throw people for a loop is that you can determine message content with high likelihood without an apparent physical connection. But even that is nothing new in principle: When a sender transmits a data block followed by a checksum over a noisy channel, we will know that checksum with high likelihood even before it has been transmitted (and with certainty, if the channel is noiseless). The reverse happens when during cryptographic communication both sides exchange a session key and then generate a bit stream from it: the bit stream is completely predictable on both sides; thus, once the session key has been transmitted securely, the bit stream does not need to be transmitted by a physical process, but is inferred by the receiving end (in mathematical terms, that works because the bit stream does not reduce information entropy). By exchanging entangled particles, we do something similar. The above should not be read to imply that nothing interesting is taking place when using the quantum-mechanical approach. According to the experiment (correct me if I’m wrong, I’m not a physicist), it basically allows you to determine for independent random events x1 and x2 two values y1 and y2 such that p(x1, y1, x2, y2) holds for a certain non-trivial predicate p with high likelihood. That in itself is remarkable without an apparent physical connection; but I don’t see how you can, based on any existing definition somewhere in the scientific literature that I am aware of, say that no communication is taking place and I don’t see how it should affect game theory.

By: Jack

Jack — Sat, 23 Oct 2004 12:43:13 +0000

Or they could bring cell phones. I think there is some signalling done by the choice of polarity to examine the electron with. In any case it is clear that information is being exchanged because if I have, say, a thousand tests I can send more bits with a given level of reliability using he quantum technique than with the prearranged system alone. If this is indeed true and all the maths has been done properly there is an action at a distance issue but I still don’t see the game theory issue. There are some issues in computability where quantum machines can make certain calculations with a significantly greater speed/lower order of growth than purely classical machines but here it seems to be purely about communication as Daniel originally said. Communication is happening because I can use the greater probabilities of transmitting a chosen bit to convey more information in a given time. This is not, except for its speed, a particularly quantum issue. I can mimic the device classically given a very little time.

By: Stephen Bullock

Stephen Bullock — Sat, 23 Oct 2004 11:44:06 +0000

Hi Matt: In the EPR example, as far as I can tell, A and B do not communicate with one another. Rather, isn’t the guy who originally entangled the two particles at least something like a broadcasting intermediary? ———————o——————————So the classical players can meet a week before the game starts to contrive who says yes and who says no. If suitable devices exist, why couldn’t quantum-enabled players bring a thousand quantum bits each to this meeting, entangle them, load them afterwards into their two personally owned qubit storage devices and then play the game with them a week later?

By: Jack

Jack — Sat, 23 Oct 2004 11:15:06 +0000

I can’t see that there is any game theory content to this beyond the use of a slightly unreliable messenger. The real puzzle would be the apparent speed of communication but I think that is at least partially illusory. It’s rather like looking at the same thing at the same time. There is real oddness is how the way you look at things at one end has an effect on the way things appear at the other but I’m not sure what that has to do with game theory. I’d be more interested in something like a quantum minority game agent. Could you make a good one with fewer bits of memory than normal? The game has to be sufficiently complicated that simple prepared responses do not have 100% success and this is probably the simplest example.