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Register a new userUncertainty and complementarity relations based on generalized skew information
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Uncertainty relations and complementarity relations are core issues in quantum mechanics and quantum information theory. By use of the generalized Wigner-Yanase-Dyson (GWYD) skew information, we derive several uncertainty and complementarity relations with respect to mutually unbiased measurements (MUMs), and general symmetric informationally complete positive operator valued measurements (SIC-POVMs), respectively. Our results include some existing ones as particular cases. We also exemplify our results by providing a detailed example.
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In this paper, we use certain norm inequalities to obtain new uncertain relations based on the Wigner-Yanase skew information. First for an arbitrary finite number of observables we derive an uncertainty relation outperforming previous lower bounds. We then propose new weighted uncertainty relations for two noncompatible observables. Two separable criteria via skew information are also obtained.
Uncertainty relation is a core issue in quantum mechanics and quantum information theory. We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalizedWigner-Yanase-Dyson (MWGWYD) skew information, and establish new uncertainty relations in terms of the MGWYD skew information and MWGWYD skew information.
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.
We present a new uncertainty relation by defining a measure of uncertainty based on skew information. For bipartite systems, we establish uncertainty relations with the existence of a quantum memory. A general relation between quantum correlations and tight bounds of uncertainty has been presented.
We establish a rigorous quantitative connection between (i) the interferometric duality relation for which-way information and fringe visibility and (ii) Heisenbergs uncertainty relation for position and modular momentum. We apply our theory to atom interferometry, wherein spontaneously emitted photons provide which way information, and unambiguously resolve the challenge posed by the metamaterial `perfect lens to complementarity and to the Heisenberg-Bohr interpretation of the Heisenberg microscope thought experiment.
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