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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, nEPR 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 qubiti, and the other is told to play games on qubitsi, j, without knowing which index isi. The test is robust: a success probability withinδof optimal guarantees distanceO (n5/2δ) fromnEPR states. However, the test does not tolerate constantδ; it breaks down forδ=Ω~ (1/n). We give an adversarial strategy that succeeds within delta of the optimum probability using onlyO~ (δ−2) EPR states.
Chao et al. (Mon,) studied this question.