Test for a large amount of entanglement, using few measurements

Abstract

Bell-inequality violations establish that two systems share some quantum entanglement. We give a simple test to certify that two systems share an asymptotically large amount of entanglement, n EPR states. The test is efficient: unlike earlier tests that play many games, in sequence or in parallel, our test requires only one or two CHSH games. One system is directed to play a CHSH game on a random specified qubit i, and the other is told to play games on qubits {i,j}, without knowing which index is i. The test is robust: a success probability within delta of optimal guarantees distance O(n^{5/2} sqrt{delta}) from n EPR states. However, the test does not tolerate constant delta; it breaks down for delta = Omega~(1/sqrt{n}). We give an adversarial strategy that succeeds within delta of the optimum probability using only O~(delta^{-2}) EPR states.

17 pages, 2 figures. Journal version

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• A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations
• Entanglement in non-local games and the hyperlinear profile of groups
• Device-independent certification of tensor products of quantum states using single-copy self-testing protocols
• Parallel Self-Testing of the GHZ State with a Proof by Diagrams
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• Nonlocal Games, Compression Theorems, and the Arithmetical Hierarchy
• A three-player coherent state embezzlement game
• Practical parallel self-testing of Bell states via magic rectangles
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• Quantum dimension test using the uncertainty principle