Device-Independent Entanglement Certification of All Entangled States.

We present a method to certify the entanglement of all entangled quantum states in a device-independent way. This is achieved by placing the state in a quantum network and constructing a correlation inequality based on an entanglement witness for the state. Our method is device independent, in the sense that entanglement can be certified from the observed statistics alone, under minimal assumptions on the underlying physics. Conceptually, our results borrow ideas from the field of self-testing to bring the recently introduced measurement-device-independent entanglement witnesses into the fully device-independent regime.

[1]  Tamás Vértesi,et al.  Algorithmic Construction of Local Hidden Variable Models for Entangled Quantum States. , 2015, Physical review letters.

[2]  J. Barrett.  Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality , 2001, quant-ph/0107045.

[3]  A. Falcon.  Physics I.1 , 2018 .

[4]  Stefano Pironio,et al.  Optimal randomness certification from one entangled bit , 2015, 1505.03837.

[5]  Remigiusz Augusiak,et al.  Local hidden–variable models for entangled quantum states , 2014, 1405.7321.

[6]  M. Żukowski,et al.  Entanglement swapping of noisy states: A kind of superadditivity in nonclassicality , 2003, quant-ph/0311194.

[7]  S. Pironio,et al.  Using complete measurement statistics for optimal device-independent randomness evaluation , 2013, 1309.3930.

[8]  J. Bell.  On the Einstein-Podolsky-Rosen paradox , 1964 .

[9]  Paul Skrzypczyk,et al.  Measurement-device-independent entanglement and randomness estimation in quantum networks , 2017, 1702.04752.

[10]  S. Popescu,et al.  Which states violate Bell's inequality maximally? , 1992 .

[11]  G. Tóth,et al.  Entanglement detection , 2008, 0811.2803.

[12]  Joseph Bowles,et al.  Self-testing of Pauli observables for device-independent entanglement certification , 2018, Physical Review A.

[13]  Nicolas Gisin,et al.  Imperfect measurement settings: Implications for quantum state tomography and entanglement witnesses , 2012, 1203.0911.

[14]  Ole Andersson,et al.  Device-independent certification of two bits of randomness from one entangled bit and Gisin's elegant Bell inequality , 2017, 1707.00564.

[15]  M. Curty,et al.  Measurement-device-independent quantum key distribution. , 2011, Physical review letters.

[16]  Eric G. Cavalcanti,et al.  Entanglement verification and steering when Alice and Bob cannot be trusted , 2012, 1210.6051.

[17]  Valerio Scarani,et al.  Nonlocality tests enhanced by a third observer. , 2012, Physical review letters.

[18]  Nicolas Brunner,et al.  Sufficient criterion for guaranteeing that a two-qubit state is unsteerable , 2015, 1510.06721.

[19]  V. Scarani,et al.  Quantum networks reveal quantum nonlocality. , 2010, Nature communications.

[20]  D Cavalcanti,et al.  General Method for Constructing Local Hidden Variable Models for Entangled Quantum States. , 2015, Physical review letters.

[21]  G. Tóth,et al.  Noise robustness of the nonlocality of entangled quantum states. , 2007, Physical review letters.

[22]  Antonio Acin,et al.  Genuine tripartite entangled states with a local hidden-variable model , 2006 .

[23]  A. Acín,et al.  Simulating Positive-Operator-Valued Measures with Projective Measurements. , 2016, Physical review letters.

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

[25]  H Zbinden,et al.  Resource-Efficient Measurement-Device-Independent Entanglement Witness. , 2015, Physical review letters.

[26]  Rodrigo Gallego,et al.  Device-independent tests of classical and quantum dimensions. , 2010, Physical review letters.

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

[28]  R. Sarpong,et al.  Bio-inspired synthesis of xishacorenes A, B, and C, and a new congener from fuscol† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c9sc02572c , 2019, Chemical science.

[29]  Werner,et al.  Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. , 1989, Physical review. A, General physics.

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

[31]  Francesco Buscemi,et al.  All entangled quantum states are nonlocal. , 2011, Physical review letters.

[32]  Mann,et al.  Maximal violation of Bell inequalities for mixed states. , 1992, Physical review letters.

[33]  A C Doherty,et al.  Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox. , 2007, Physical review letters.

[34]  Nicolas Gisin,et al.  Measurement-device-independent entanglement witnesses for all entangled quantum states. , 2012, Physical review letters.

[35]  Marco T'ulio Quintino,et al.  Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$ , 2016, 1609.06114.