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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 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.Comment: 17 pages, 2 figures. Journal versio
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