Tight State-Independent Uncertainty Relations for Qubits

Alastair A. Abbott, Pierre-Louis Alzieu, Michael J. W. Hall and Cyril Branciard
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Alastair A. Abbott: Institut Néel, CNRS and Université Grenoble Alpes, 38042 Grenoble Cedex 9, France
Pierre-Louis Alzieu: Institut Néel, CNRS and Université Grenoble Alpes, 38042 Grenoble Cedex 9, France
Michael J. W. Hall: Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane 4111, Australia
Cyril Branciard: Institut Néel, CNRS and Université Grenoble Alpes, 38042 Grenoble Cedex 9, France

Mathematics, 2016, vol. 4, issue 1, 1-17

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.

Keywords: uncertainty relations; state-independence; quantum measurement (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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