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Quantum Sequential Hypothesis Testing.

Esteban Martínez Vargas1, Christoph Hirche2, Gael Sentís1

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

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Summary
This summary is machine-generated.

We introduce sequential analysis for quantum hypothesis testing, finding optimal lower bounds on the number of quantum states needed. This method, particularly for qubit states, surpasses fixed-copy strategies, even achieving perfect discrimination for pure states.

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Area of Science:

  • Quantum Information Processing
  • Quantum Physics
  • Statistical Inference

Background:

  • Quantum hypothesis testing is crucial for distinguishing quantum states.
  • Current methods often require a predetermined number of quantum state copies.
  • Achieving high accuracy in state discrimination is computationally demanding.

Purpose of the Study:

  • To introduce sequential analysis for quantum hypothesis testing.
  • To determine the ultimate lower bounds on the average number of quantum state copies required.
  • To develop strategies that achieve these lower bounds.

Main Methods:

  • Sequential analysis applied to quantum hypothesis testing.
  • Derivation of lower bounds on the average number of copies.
  • Development of a block-sampling strategy.
  • Analysis of strategies for qubit and general quantum states.

Main Results:

  • Ultimate lower bounds on the average number of copies for quantum state discrimination were established.
  • A block-sampling strategy achieves these bounds for certain state classes.
  • Sequential strategies, especially for qubit states using local measurements, outperform collective measurements on fixed copies.
  • For pure states, finite average samples are needed even for perfect discrimination (ε=0).

Conclusions:

  • Sequential analysis provides an optimal approach to quantum hypothesis testing.
  • The derived bounds offer fundamental limits on resources for quantum state discrimination.
  • Practical strategies exist that can achieve these optimal bounds, improving efficiency.