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Thermodynamic bound on quantum state discrimination.

José Polo-Gómez1

  • 1Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1; Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1; and Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5.

Physical Review. E
|February 17, 2024
PubMed
Summary
This summary is machine-generated.

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The second law of thermodynamics limits how accurately quantum states can be distinguished. This study establishes a thermodynamic bound on quantum state discrimination accuracy, highlighting a key difference between thermodynamic and quantum entropy measures.

Area of Science:

  • Quantum Information Theory
  • Thermodynamics
  • Statistical Mechanics

Background:

  • Quantum state discrimination is crucial for quantum information processing.
  • The second law of thermodynamics governs energy transfer and entropy.
  • Previous work explored connections between thermodynamics and quantum information, but limitations remain.

Purpose of the Study:

  • To investigate the thermodynamic constraints on quantum state discrimination accuracy.
  • To establish a nontrivial upper bound on discrimination accuracy based on thermodynamic principles.
  • To explore the relationship between thermodynamic entropy and von Neumann entropy.

Main Methods:

  • Analysis of an ideal gas with internal quantum degrees of freedom.
  • Application of a thermodynamic cycle based on Peres' proposal.

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  • Derivation of a thermodynamic bound on quantum state discrimination.

    • Main Results:

    • A nontrivial upper bound on quantum state discrimination accuracy was established.
    • This bound relies on the linearity of quantum mechanics and no-work-extraction constraint.
    • The thermodynamic bound matches Holevo's bound on accessible information but is looser than the Holevo-Helstrom bound.

    Conclusions:

    • The second law of thermodynamics imposes fundamental limits on quantum state discrimination.
    • Results provide evidence for the disagreement between thermodynamic and von Neumann entropy.
    • The findings may impose limitations on theories beyond standard quantum mechanics.