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Mathematics 2016, 4(1), 8; doi:10.3390/math4010008

Tight State-Independent Uncertainty Relations for Qubits

1
Institut Néel, CNRS and Université Grenoble Alpes, 38042 Grenoble Cedex 9, France
2
Ecole Normale Supérieure de Lyon, 69342 Lyon, France
3
Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane 4111, Australia
*
Authors to whom correspondence should be addressed.
Academic Editors: Paul Busch, Takayuki Miyadera and Teiko Heinosaari
Received: 9 December 2015 / Revised: 22 January 2016 / Accepted: 17 February 2016 / Published: 24 February 2016
(This article belongs to the Special Issue Mathematics of Quantum Uncertainty)
View Full-Text   |   Download PDF [667 KB, uploaded 24 February 2016]   |  

Abstract

The well-known Robertson–Schrödinger uncertainty relations have state-dependent lower bounds, which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit measurements that completely characterise the obtainable uncertainty values. This approach can give such relations for any number of observables, and we do so explicitly for arbitrary pairs and triples of qubit measurements. We show how these relations can be transformed into equivalent tight entropic uncertainty relations. More generally, they can be expressed in terms of any measure of uncertainty that can be written as a function of the expectation value of the observable for a given state. View Full-Text
Keywords: uncertainty relations; state-independence; quantum measurement uncertainty relations; state-independence; quantum measurement
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Abbott, A.A.; Alzieu, P.-L.; Hall, M.J.W.; Branciard, C. Tight State-Independent Uncertainty Relations for Qubits. Mathematics 2016, 4, 8.

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