4 ms·

You have narrowed in on the exact point of the game: Alice and Bob can pre-share arbitrary amounts of classical information and still not win more than 89% of

by dfdz 7y ago

You have narrowed in on the exact point of the game: Alice and Bob can pre-share arbitrary amounts of classical information and still not win more than 89% of the time. What would your strategy be for sharing information before the game starts?

bscphil 7y ago
Well, that's sort of the point most of us seem to be making here. We don't understand, and more importantly, the excerpt doesn't explain, how sharing an entangled particle pair (from which you can generate two infinite streams of identical information on both sides) is interestingly different than sharing a seed to an RNG (from which you can generate two infinite streams of identical information on both sides). They're apparently the same phenomenon, so asking people to think about the game without explaining what the difference is means you haven't really explained what's going on.
- AstralStorm 7y ago
  There are two random choices. One of the value, the other by the verifier. There are infinitely many columns and rows to check, which would require an infinite amount of shared RNG. (or is otherwise finite, a PRNG) Yet this can be done in MIP* because state in A and B is correlated for any state. The problem can be rephrased as "does there exist an ideal PRNG that is not discernible from a true quantum RNG". Discerning between real RNG and PRNG is akin to solving the halting problem and one of the lynchpins if the proof.
- titanomachy 7y ago
  The comments here led me to realize that I didn't really understand, either. Thank you. To save you some searching, I found the answer here [1]. The crux is that Alice and Bob don't know which row/column the other is filling, and they are given symbol-selection rules which would contradict each other if used to fill the whole square, preventing a pre-ordained strategy (e.g. a pre-seeded RNG) with 100% success rate. So a 100% strategy would intuitively need some way of communicating _after_ they are given their row and column, and the math shows that the quasi-communication granted by entanglement is sufficient. I'm sure my explanation is also insufficient, but there should be enough information at the link to convince you if you're curious. [1] https://en.wikipedia.org/wiki/Quantum_pseudo-telepathy#The_Mermin%E2%80%93Peres_magic_square_game https://en.wikipedia.org/wiki/Quantum_pseudo-telepathy#The_M...
  - bscphil 7y ago
    This is great, thanks.
- wtallis 7y ago
  > [...] how sharing an entangled particle pair (...) is interestingly different than sharing a seed to an RNG > They're apparently the same phenomenon You're the one deciding that they're the same phenomenon, by choosing to only imagine using the entangled particle pair to seed a PRNG on each side using the same method. The key thing to realize is that Alice and Bob have quantum mutual information, not classical, and that "quantum" here is not just technobabble but actually has meaningful consequences. If Alice and Bob choose to destroy the quantum information and extract the same bit(s) of classical information from their respective halves of the entangled pair(s) before the game starts, then the quantum case has been reduced to the classical case and you can think of them as the same phenomenon. But if instead they keep the quantum information around past the start of the game and decide what to do with it based on the hand they're dealt, they can get a win rate that's impossible with only pre-shared classical information.
  - bscphil 7y ago
    To be clear, I wasn't saying they were the same phenomenon. I was saying they're apparently the same phenomenon, even though I know they can't really be. My opinion was that it was the responsibility of the article to explain why these apparently identical phenomena are in fact distinct.
- cyphar 7y ago
  The difference is that entangled particles cannot be modelled using a local hidden-variable theory of quantum mechanics (that's what the Bell inequalities and experimental evidence have shown). The reason why this is the case is a more involved question which I tried my best to explain in [1]. So entangled particles give you fundamentally different properties to a seed to an RNG (or any other arbitrary local hidden-variable setup you can come up with). [1]: https://news.ycombinator.com/item?id=22490693 https://news.ycombinator.com/item?id=22490693
- doctoboggan 7y ago
  The "interesting" thing is that entangled particles allow the player to win 100% of the time. There is _no way_ sharing only classical information before the game to guarantee 100% win rate.

by dfdz 7y ago

bscphil 7y ago

Well, that's sort of the point most of us seem to be making here. We don't understand, and more importantly, the excerpt doesn't explain, how sharing an entangled particle pair (from which you can generate two infinite streams of identical information on both sides) is interestingly different than sharing a seed to an RNG (from which you can generate two infinite streams of identical information on both sides). They're apparently the same phenomenon, so asking people to think about the game without explaining what the difference is means you haven't really explained what's going on.

AstralStorm 7y ago
There are two random choices. One of the value, the other by the verifier. There are infinitely many columns and rows to check, which would require an infinite amount of shared RNG. (or is otherwise finite, a PRNG) Yet this can be done in MIP* because state in A and B is correlated for any state. The problem can be rephrased as "does there exist an ideal PRNG that is not discernible from a true quantum RNG". Discerning between real RNG and PRNG is akin to solving the halting problem and one of the lynchpins if the proof.
titanomachy 7y ago
The comments here led me to realize that I didn't really understand, either. Thank you. To save you some searching, I found the answer here [1]. The crux is that Alice and Bob don't know which row/column the other is filling, and they are given symbol-selection rules which would contradict each other if used to fill the whole square, preventing a pre-ordained strategy (e.g. a pre-seeded RNG) with 100% success rate. So a 100% strategy would intuitively need some way of communicating _after_ they are given their row and column, and the math shows that the quasi-communication granted by entanglement is sufficient. I'm sure my explanation is also insufficient, but there should be enough information at the link to convince you if you're curious. [1] https://en.wikipedia.org/wiki/Quantum_pseudo-telepathy#The_Mermin%E2%80%93Peres_magic_square_game https://en.wikipedia.org/wiki/Quantum_pseudo-telepathy#The_M...
- bscphil 7y ago
  This is great, thanks.
wtallis 7y ago
> [...] how sharing an entangled particle pair (...) is interestingly different than sharing a seed to an RNG > They're apparently the same phenomenon You're the one deciding that they're the same phenomenon, by choosing to only imagine using the entangled particle pair to seed a PRNG on each side using the same method. The key thing to realize is that Alice and Bob have quantum mutual information, not classical, and that "quantum" here is not just technobabble but actually has meaningful consequences. If Alice and Bob choose to destroy the quantum information and extract the same bit(s) of classical information from their respective halves of the entangled pair(s) before the game starts, then the quantum case has been reduced to the classical case and you can think of them as the same phenomenon. But if instead they keep the quantum information around past the start of the game and decide what to do with it based on the hand they're dealt, they can get a win rate that's impossible with only pre-shared classical information.
- bscphil 7y ago
  To be clear, I wasn't saying they were the same phenomenon. I was saying they're apparently the same phenomenon, even though I know they can't really be. My opinion was that it was the responsibility of the article to explain why these apparently identical phenomena are in fact distinct.
cyphar 7y ago
The difference is that entangled particles cannot be modelled using a local hidden-variable theory of quantum mechanics (that's what the Bell inequalities and experimental evidence have shown). The reason why this is the case is a more involved question which I tried my best to explain in [1]. So entangled particles give you fundamentally different properties to a seed to an RNG (or any other arbitrary local hidden-variable setup you can come up with). [1]: https://news.ycombinator.com/item?id=22490693 https://news.ycombinator.com/item?id=22490693
doctoboggan 7y ago
The "interesting" thing is that entangled particles allow the player to win 100% of the time. There is _no way_ sharing only classical information before the game to guarantee 100% win rate.