Analytic robustness bound for self-testing of the singlet with two binary measurements

Self-testing refers to a way of uniquely identifying an uncharacterized quantum device based solely on certain extremal quantum correlations. It is known that in the ideal case of a two-qubit singlet all the extremal points that can be obtained by measuring the singlet form the whole criteria for self-testing the singlet and the associated measurements. To make these self-testing criteria more suitable for practical applications, relevant robustness bounds are necessary to discuss. However, the previous robustness analyses for these criteria were obtained by the swap method, which may not be guaranteed to be tight. In this paper, we construct a general extraction map applying to all self-testing criteria of the singlet state with two binary measurements for each party and derive analytic robustness bounds for a self-testing singlet in different regions of the boundary of the extremal quantum correlation set. The comparison shows that our robustness bounds are better than the known results and close to optimal for these self-testing criteria of a singlet state with two binary measurements.

[1]  Matthew McKague,et al.  Self-Testing Graph States , 2010, TQC.

[2]  S. Massar,et al.  Device-independent state estimation based on Bell’s inequalities , 2009, 0907.2170.

[3]  S. Wehner,et al.  Publisher's Note: Bell nonlocality [Rev. Mod. Phys. 86, 419 (2014)] , 2014 .

[4]  Fei Gao,et al.  Reduced gap between observed and certified randomness for semi-device-independent protocols , 2015 .

[5]  L. Masanes.  Asymptotic violation of Bell inequalities and distillability. , 2005, Physical review letters.

[6]  Miguel Navascues,et al.  Device-independent tomography of multipartite quantum states , 2014, 1407.5911.

[7]  Adrian Kent,et al.  Private randomness expansion with untrusted devices , 2010, 1011.4474.

[8]  Wen-Hao Zhang,et al.  Experimentally Robust Self-testing for Bipartite and Tripartite Entangled States. , 2018, Physical review letters.

[9]  A. Acín,et al.  A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations , 2008, 0803.4290.

[10]  Miguel Navascues,et al.  Robust Self Testing of Unknown Quantum Systems into Any Entangled Two-Qubit States , 2013 .

[11]  Stefano Pironio,et al.  Random numbers certified by Bell’s theorem , 2009, Nature.

[12]  V. Scarani,et al.  Device-independent security of quantum cryptography against collective attacks. , 2007, Physical review letters.

[13]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[14]  G. Paul,et al.  Device Independent Quantum Private Query , 2017, 1701.01087.

[15]  Jędrzej Kaniewski,et al.  Analytic and Nearly Optimal Self-Testing Bounds for the Clauser-Horne-Shimony-Holt and Mermin Inequalities. , 2016, Physical review letters.

[16]  T. H. Yang,et al.  Robust self-testing of the singlet , 2012, 1203.2976.

[17]  Valerio Scarani,et al.  All the self-testings of the singlet for two binary measurements , 2015, 1511.04886.

[18]  Jean-Daniel Bancal,et al.  Physical characterization of quantum devices from nonlocal correlations , 2013, 1307.7053.

[19]  Miguel Navascués,et al.  Robust and versatile black-box certification of quantum devices. , 2014, Physical review letters.

[20]  V. Scarani,et al.  Device-independent quantum key distribution secure against collective attacks , 2009, 0903.4460.

[21]  Jean-Daniel Bancal,et al.  Robust self testing of the 3-qubit W state , 2014, 1407.5769.

[22]  A. Acín,et al.  Secure device-independent quantum key distribution with causally independent measurement devices. , 2010, Nature communications.

[23]  Bin Liu,et al.  A Generic Construction of Quantum-Oblivious-Key-Transfer-Based Private Query with Ideal Database Security and Zero Failure , 2017, IEEE Transactions on Computers.