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Discrimination Power of a Quantum Detector.

Christoph Hirche1, Masahito Hayashi2,3, Emilio Bagan1

  • 1Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain.

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Summary
This summary is machine-generated.

This study quantifies the ultimate discrimination power of quantum measurement devices. We establish fundamental bounds on error probabilities, revealing optimal strategies for distinguishing quantum states.

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Area of Science:

  • Quantum Information Science
  • Quantum Measurement Theory
  • Statistical Inference

Background:

  • Distinguishing quantum states is crucial for quantum information processing.
  • Existing methods often optimize over measurements for fixed states, or vice-versa.
  • Quantifying the intrinsic error of a measurement device is essential for its practical application.

Purpose of the Study:

  • To determine the fundamental limits of a quantum measurement device's ability to discriminate between two quantum states.
  • To quantify the intrinsic error associated with a measurement device.
  • To explore the impact of multiple measurements and data processing on discrimination power.

Main Methods:

  • Minimizing error probabilities (averaged and constrained) over all possible n-partite input states.
  • Deriving asymptotic rates of error decrease for large numbers of measurements (n).
  • Establishing Chernoff-type and dual Stein's lemma/Hoeffding bounds for discrimination limits.

Main Results:

  • Identical copies of input states are optimal for asymptotic discrimination.
  • Derived Chernoff-type bounds for averaged error rates, dual to standard Chernoff bounds.
  • Obtained optimal asymptotic rates for constrained error probabilities, dual to Stein's lemma and Hoeffding's bound.
  • Demonstrated that adaptive protocols do not enhance asymptotic discrimination rates.

Conclusions:

  • The derived asymptotic rates quantify the ultimate discrimination power of any quantum measurement device.
  • These findings provide fundamental benchmarks for the performance of quantum measurement devices.
  • The study highlights the importance of state preparation in optimizing quantum discrimination tasks.