Test for a large amount of entanglement, using few measurements

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 δ of optimal guarantees distance O(n √ δ) from n EPR states. However, the test does not tolerate constant δ; it breaks down for δ = Ω̃(1/ √ n). We give an adversarial strategy that succeeds within δ of the optimum probability using only Õ(δ−2) EPR states.