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Uncertainty Relations for Quantum Coherence

Author

Listed:
  • Uttam Singh

    (Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India)

  • Arun Kumar Pati

    (Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India)

  • Manabendra Nath Bera

    (ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, ES-08860 Castelldefels, Spain)

Abstract

Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can there be some trade-off relation between the coherence measures in different reference bases? We show that the quantum coherence of a state as quantified by the relative entropy of coherence in two or more noncommuting reference bases respects uncertainty like relations for a given state of single and bipartite quantum systems. In the case of bipartite systems, we find that the presence of entanglement may tighten the above relation. Further, we find an upper bound on the sum of the relative entropies of coherence of bipartite quantum states in two noncommuting reference bases. Moreover, we provide an upper bound on the absolute value of the difference of the relative entropies of coherence calculated with respect to two incompatible bases.

Suggested Citation

  • Uttam Singh & Arun Kumar Pati & Manabendra Nath Bera, 2016. "Uncertainty Relations for Quantum Coherence," Mathematics, MDPI, vol. 4(3), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:3:p:47-:d:74129
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    References listed on IDEAS

    as
    1. Michał Horodecki & Jonathan Oppenheim, 2013. "Fundamental limitations for quantum and nanoscale thermodynamics," Nature Communications, Nature, vol. 4(1), pages 1-6, October.
    2. Paul Skrzypczyk & Anthony J. Short & Sandu Popescu, 2014. "Work extraction and thermodynamics for individual quantum systems," Nature Communications, Nature, vol. 5(1), pages 1-8, September.
    3. Matteo Lostaglio & David Jennings & Terry Rudolph, 2015. "Description of quantum coherence in thermodynamic processes requires constraints beyond free energy," Nature Communications, Nature, vol. 6(1), pages 1-9, May.
    4. Varun Narasimhachar & Gilad Gour, 2015. "Low-temperature thermodynamics with quantum coherence," Nature Communications, Nature, vol. 6(1), pages 1-6, November.
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