Test for a large amount of entanglement, using few measurements

Rui Chao1, Ben W. Reichardt1, Chris Sutherland1, and Thomas Vidick2

1University of Southern California
2California Institute of Technology

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 $\delta = \tilde\Omega (1/\sqrt{n})$. We give an adversarial strategy that succeeds within delta of the optimum probability using only $\tilde O(\delta^{-2})$ EPR states.

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► References

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Cited by

[1] Spencer Breiner, Amir Kalev, and Carl A. Miller, "Parallel Self-Testing of the GHZ State with a Proof by Diagrams", Electronic Proceedings in Theoretical Computer Science 287, 43 (2019).

[2] Rotem Arnon-Friedman and Jean-Daniel Bancal, "Device-independent certification of one-shot distillable entanglement", New Journal of Physics 21 3, 033010 (2019).

[3] Andrea Coladangelo, "Generalization of the Clauser-Horne-Shimony-Holt inequality self-testing maximally entangled states of any local dimension", Physical Review A 98 5, 052115 (2018).

[4] Jedrzej Kaniewski, "Self-testing of binary observables based on commutation", Physical Review A 95 6, 062323 (2017).

[5] Rotem Arnon-Friedman and Henry Yuen, "Noise-tolerant testing of high entanglement of formation", arXiv:1712.09368.

[6] Joseph Fitzsimons, Zhengfeng Ji, Thomas Vidick, and Henry Yuen, "Quantum proof systems for iterated exponential time, and beyond", arXiv:1805.12166.

[7] Rui Chao, Ben W. Reichardt, Chris Sutherland, and Thomas Vidick, "Overlapping qubits", arXiv:1701.01062.

[8] Zhengfeng Ji, Debbie Leung, and Thomas Vidick, "A three-player coherent state embezzlement game", arXiv:1802.04926.

The above citations are from Crossref's cited-by service (last updated 2019-06-18 22:53:44) and SAO/NASA ADS (last updated 2019-06-18 22:53:45). The list may be incomplete as not all publishers provide suitable and complete citation data.