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Quantifying the Difference between Many-Body Quantum States.

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Summary
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We introduce weighted distances, a new measure for comparing complex quantum states. This method accounts for measurement apparatus, improving evaluation of quantum devices and revealing limits on resource conversion.

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Area of Science:

  • Quantum Information Science
  • Many-Body Physics
  • Quantum Computing

Background:

  • Traditional quantum state overlap and fidelity measures are insufficient for complex many-body systems.
  • Existing metrics fail to account for the experimental setup required for state discrimination.

Purpose of the Study:

  • Introduce a new class of information-theoretic measures called weighted distances.
  • Develop a method to quantify the difficulty of discriminating between complex quantum states, considering measurement apparatus.
  • Establish a lower bound for the experimental cost of quantum transformations.

Main Methods:

  • Definition of weighted distances as a novel information-theoretic measure.
  • Incorporation of measurement apparatus structure into state discrimination quantification.
  • Derivation of the weighted Bures length as a cost bound for quantum processes.

Main Results:

  • Weighted distances effectively compare complex quantum states in many-body systems.
  • These measures allow for evaluation of theoretical and experimental performance of quantum devices.
  • The weighted Bures length provides a lower bound on the experimental cost of quantum transformations.

Conclusions:

  • Weighted distances offer a more robust approach to quantifying differences between complex quantum states.
  • The findings provide critical insights into the performance limitations and resource costs of quantum devices.
  • This work establishes a fundamental quantum limit on converting physical resources into computational ones.