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Quantum Fidelity for Arbitrary Gaussian States.

Leonardo Banchi1, Samuel L Braunstein2, Stefano Pirandola2

  • 1Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom.

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Summary
This summary is machine-generated.

We developed a formula for quantum fidelity between Gaussian states using statistical moments. This advances quantum metrology and continuous-variable protocols with multiple modes.

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Area of Science:

  • Quantum Information Science
  • Quantum Optics
  • Statistical Mechanics

Background:

  • Calculating quantum fidelity for multimode Gaussian states is complex.
  • Existing methods are often limited to one- or two-mode systems.
  • Need for efficient tools in quantum metrology and hypothesis testing.

Purpose of the Study:

  • Derive a computable analytical formula for quantum fidelity between arbitrary multimode Gaussian states.
  • Express this formula using first- and second-order statistical moments.
  • Adapt the formula for use with symplectic invariants.

Main Methods:

  • Analytical derivation based on statistical moments of Gaussian states.
  • Representation of the fidelity formula using symplectic invariants.
  • Application of the formula to derive closed forms for Bures metric and quantum Fisher information.

Main Results:

  • A simple, computable analytical formula for multimode Gaussian state fidelity.
  • The formula is expressed in terms of first- and second-order statistical moments.
  • Closed-form expressions for Bures metric and quantum Fisher information derived.

Conclusions:

  • The derived formula simplifies fidelity calculations for complex quantum systems.
  • Enables extension of continuous-variable protocols beyond two-mode analysis.
  • Provides a powerful tool for quantum metrology and hypothesis testing with multimode Gaussian resources.