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Tight State-Independent Uncertainty Relations for Qubits

Author

Listed:
  • 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
    Ecole Normale Supérieure de Lyon, 69342 Lyon, 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)

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.

Suggested Citation

  • Alastair A. Abbott & Pierre-Louis Alzieu & Michael J. W. Hall & Cyril Branciard, 2016. "Tight State-Independent Uncertainty Relations for Qubits," Mathematics, MDPI, vol. 4(1), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:1:p:8-:d:64333
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