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arXiv:1412.4010 · Communications in Mathematical Physics

Sampling Quantum Nonlocal Correlations with High Probability

C. E. González-Guillén, C. H. Jiménez, C. Palazuelos, I. Villanueva

Published Apr 18, 2016• 7 citations
arXivHTMLPDF
DOI
10.1007/s00220-016-2625-8

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Abstract We investigate the violation of nonlocal realism using various entangled continues- and hybrid-variable states under dichotomic observables. In particular, we consider two cases of dichotomic observables (1) described by a pseudospin operator and (2) given in terms of the Wigner representation of the state in phase space, parity measurement and displacement operation. We address the recently proposed operational measure of nonlocality which describes the probability of local-realism violation under randomly sampled observables. We show the usefulness and limitations of the probability of local-realism violation for the detection of nonlocality. A simple procedure to detect such nonlocal correlations for randomly chosen settings with efficiencies of up to 100% is proposed. The practical advantage of applying random measurements that considerably lowers the experimental requirements is mentioned.
The quantum nonlocal correlation of quantum states plays an important role in the quantum information and quantum computing protocols. However, during the transmission of entangled states in the quantum channel, they will inevitably interact with the environment, resulting in the degradation of the coherence and then weakening the quantum nonlocal correlation. Using a high probability quantum nonlocal correlation testing scheme based on Hardy-type paradox, in this paper we investigate the quantum nonlocal correlation testing of two-qubit polarization entangled states when they transmit through amplitude damping channel (ADC), phase damping channel (PDC) and depolarization damping channel (DC). The results show that DC has a great influence on the quantum nonlocal correlation testing, while PDC has little influence on the quantum nonlocal correlation testing of quantum states. Finally, this paper also gives condition for the successful quantum nonlocal correlation testing of ADC under weak measurement and quantum weak measurement reversal operation. The results show that when the intensity of weak measurement increases, the influence of ADC decoherence effect on quantum nonlocal correlation testing can be effectively reduced.