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Gaussian quantum states can be disentangled using symplectic rotations.

Maurice A de Gosson1

  • 1Faculty of Mathematics (NuHAG), University of Vienna, Vienna, Austria.

Letters in Mathematical Physics
|November 1, 2021
PubMed
Summary

Every Gaussian mixed quantum state can be disentangled using passive symplectic transformations. This method, leveraging the Werner-Wolf condition and Weyl quantization, offers a new approach to quantum state manipulation.

Keywords:
Density operatorDisentanglementEntanglementGaussian stateSymplectic rotation

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Area of Science:

  • Quantum Information Theory
  • Quantum Optics
  • Mathematical Physics

Background:

  • Gaussian quantum states are fundamental in quantum information.
  • Entanglement is a key resource in quantum mechanics, but its presence in mixed states can be challenging to manage.
  • Previous studies have explored methods for characterizing and manipulating quantum states.

Purpose of the Study:

  • To demonstrate that all Gaussian mixed quantum states can be disentangled.
  • To introduce a method for disentanglement using passive symplectic transformations.
  • To complement existing research on quantum state manipulation.

Main Methods:

  • Utilizing passive symplectic transformations, specifically metaplectic operators associated with symplectic rotations.
  • Applying the Werner-Wolf condition for analyzing covariance matrices of quantum states.
  • Leveraging the symplectic covariance property of Weyl quantization.

Main Results:

  • Proven that any Gaussian mixed quantum state is amenable to disentanglement via passive symplectic transformations.
  • Established a direct link between symplectic transformations and the disentanglement of Gaussian states.
  • Provided a theoretical framework complementing prior work by Lami, Serafini, and Adesso.

Conclusions:

  • Passive symplectic transformations offer a universal method for disentangling Gaussian mixed quantum states.
  • The findings provide new tools for controlling and utilizing quantum entanglement in Gaussian systems.
  • This work advances the understanding of quantum state manipulation and its theoretical underpinnings.