Device-independent parallel self-testing of two singlets

Abstract

Device-independent self-testing is the possibility of certifying the quantum state and the measurements, up to local isometries, using only the statistics observed by querying uncharacterized local devices. In this paper, we study parallel self-testing of two maximally entangled pairs of qubits: in particular, the local tensor product structure is not assumed but derived. We prove two criteria that achieve the desired result: a double use of the Clauser-Horne-Shimony-Holt inequality and the $3\times 3$ Magic Square game. This demonstrate that the magic square game can only be perfectly won by measureing a two-singlets state. The tolerance to noise is well within reach of state-of-the-art experiments.

9 pages, 2 figures

References in corpus (10)

• Device-independent security of quantum cryptography against collective attacks
• Significant-loophole-free test of Bell's theorem with entangled photons
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Bounding the set of quantum correlations
• Robust Self Testing of the Singlet
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• Robust and versatile black-box certification of quantum devices
• Robust self testing of the 3-qubit $W$ state
• Device-independent tomography of multipartite quantum states
• Self-testing in parallel

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