Games to Establish Structure in an Unknown Hilbert Space
summary
Introduces a concrete, testable claim: playing the CHSH game gives quantum devices a maximum win rate of cos^2(pi/8) ≈ 0.85 and a rigidity statement that winning near that rate forces the devices’ joint state and measurements to be close (up to local isometries) to an EPR pair. Repeating sequential CHSH blocks yields a statistical guarantee of roughly n EPR pairs, with efficiency polynomial in parameters but impractical constants (error scales like ε^{1/C}, many-round statistical losses, and quadratic blowups). Lists open problems: parallel composition, tolerance to constant noise, and rounds-with-communication.
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chapters (16)
- 0:00Motivation for experimental systems
- 3:14CHSH game as a test
- 5:47First rigidity theorem
- 8:59Limitations of rigidity theorem
- 9:41Main theorem for multiple CHSH games
- 16:26Formalizing with superoperators
- 19:17Proof structure and steps
- 21:49Tensor product structure
- 27:27Overcoming error accumulation
- 32:28Constructing tensor product strategy
- 37:23Ensuring ideal strategies
- 38:45Open questions and future work
- 42:20Quantum key distribution applications
- 45:39Connections to quantum problems
- 47:10Comparing dimension-testing approaches
- 48:25Closing remarks and Q&A
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