Test for a large amount of entanglement, using few measurements

TL;DR

This paper introduces an efficient and robust test for certifying large-scale quantum entanglement using minimal measurements, specifically one or two CHSH games, with quantifiable success guarantees.

Contribution

The paper presents a novel, simple, and efficient test for large entanglement that requires only a few measurements and provides robustness guarantees.

Findings

Test certifies asymptotically large entanglement with minimal measurements.

Success probability close to optimal guarantees proximity to n EPR states.

The test's robustness diminishes for large delta, with specific adversarial strategies analyzed.

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, 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.