Quantum uncertainty based on metric adjusted skew information

Abstract

Prompted by the open questions in Gibilisco [Int. J. Software Informatics, 8(3-4): 265, 2014], in which he introduced a family of measurement-induced quantum uncertainty measures via metric adjusted skew informations, we investigate these measures' fundamental properties (including basis independence and spectral representation), and illustrate their applications to detect quantum nonlocality and entanglement.Key words and phrases: metric adjusted skew information; operator monotone functions; quantum uncertainty; quantum nonlocality; quantum entanglement MSC2010 classification: 94A17, 81P15, 15A45.

The Hammersley–Chapman–Robbins inequality for repeatedly monitored quantum system

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