On uncertainty relations and entanglement detection with mutually unbiased measurements

Abstract

We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also revisited. First, we estimate from above the sum of the indices of coincidence for several mutually unbiased measurements. Further, we derive entropic uncertainty relations in terms of the Rényi and Tsallis entropies. Both the state-dependent and state-independent formulations are obtained. Using the two sets of local mutually unbiased measurements, a method of entanglement detection in bipartite finite-dimensional systems may be realized. A certain trade-off between a sensitivity of the scheme and its experimental complexity is discussed.

arXiv comment13 pages, no figures. Minor improvements. Typos fixed

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• Improved separability criteria via some classes of measurements
• On the Brukner-Zeilinger approach to information in quantum measurements
• Separability conditions based on local fine-grained uncertainty relations
• Rényi formulation of uncertainty relations for POVMs assigned to a quantum design
• Separability criteria via some classes of measurements
• Every entangled state provides an advantage in classical communication
• On entropic uncertainty relations for measurements of energy and its "complement"
• Uncertainty relations for quantum measurements from generalized equiangular tight frames
• Entropic uncertainty relations for multiple measurements assigned with biased weights
• On Kirkwood--Dirac quasiprobabilities and unravelings of quantum channel assigned to a tight frame
• Generalization of Pauli channels through mutually unbiased measurements
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• General framework of quantum complementarity from a measurement-based perspective
• Tight bounds from multiple-observable entropic uncertainty relations
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