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.
Highlights
Entanglement separates quantum from classical physics, and is a key source for the power of quantum-mechanical devices
Following the rules of the CHSH game [CHSH69], they ask random questions to the two systems—electrons separated by over a kilometer in [H+15]—and security is based on the space-like separation of the measurements giving the answers
We show that p√assing our test with probability within δ of the optimal value implies that the systems are O(n5/2 δ) close to n EPR states
Summary
Entanglement separates quantum from classical physics, and is a key source for the power of quantum-mechanical devices. Chaining together pairwise statements like this establishes that they share n EPR states Note that this test requires very little processing to test a high-dimensional quantum state, as the number of possible operations to be performed scales quadratically with the number of qubits tested. Our main result is based on the CHSH test and the use of EPR states, we show in Appendix A that the result can be generalized to separate qubits via any two-qubit state entangled across HA ⊗ HB. The optimal success probability for this game is 1, which allows for a more efficient analysis in comparison to the CHSH game They require fewer experiments to achieve certain statistical confidence. Robust protocols certifying a large amount of entanglement, without explicitly certifying that the state must be (close to) maximally entangled, are provided in [CS17, AY17, AB17]
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