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,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 qubits{i,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.