Number-phase entanglement and Einstein-Podolsky-Rosen steering

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Fadel, Matteo
He, Qiongyi
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American Physical Society
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We use the uncertainty relation between the operators associated with the total number of particles and with the relative phase of two bosonic modes to construct entanglement and Einstein-Podolsky-Rosen steering criteria. These can be tested experimentally in a variety of systems, such as optical fields, Bose-Einstein condensates, and mechanical oscillators. While known entanglement criteria involving the phase observable typically require us to perform interference measurements by recombining the two systems, our criteria can be tested through local measurements at two spatially distinct positions to investigate the nonlocal nature of quantum correlations. We present simple examples where our criteria are violated and show their robustness to noise. Apart from being useful for state characterization, they might find application in quantum information protocols, for example, based on number-phase teleportation.
©2020 American Physical Society. M.F. acknowledges support from the National Natural Science Foundation of China (Grants No. 11622428 and No. 61675007) and from the Swiss National Science Foundation. Q.H. is thankful for the support from the National Natural Science Foundation of China (Grants No. 61675007 and No. 11975026), Beijing Natural Science Foundation (Grant No. Z190005), and the Key R&D Program of Guangdong Province (Grant No. 2018B030329001). L.A. and A.L. acknowledge financial support from Spanish Ministerio de Economía y Competitividad Project No. FIS2016-75199-P. L.A. acknowledges financial support from the European Social Fund and the Spanish Ministerio de Ciencia Innovación y Universidades, Contract Grant No. BES-2017-081942.