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Filter functions for the Glauber-Sudarshan P-function regularization

Mani Zartab1,2, Ezad Shojaee3,4, and Saleh Rahimi-Keshari1,5

  • 1Department of Physics, University of Tehran, P.O. Box 14395-547, Tehran, Iran
  • 2Física Teórica: Informaciò i Fenómens Quàntics, Departament de Física, Universitat Autónoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
  • 3National Institute of Standards and Technology, Boulder, Colorado 80305, USA
  • 4Department of Physics, University of Colorado, Boulder, Colorado, 80309, USA
  • 5School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran

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Phys. Rev. A 107, 053706 – Published 10 May, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.053706

Abstract

The phase-space quasiprobability distribution formalism for representing quantum states provides practical tools for various applications in quantum optics such as identifying the nonclassicality of quantum states. We study filter functions that are introduced to regularize the Glauber-Sudarshan P function. We show that the quantum map associated with a filter function is completely positive and trace preserving and hence physically realizable if and only if the Fourier transform of this function is a probability density distribution. We also derive a lower bound on the fidelity between the input and output states of a physical quantum filtering map. Therefore, based on these results, we show that any quantum state can be approximated, to arbitrary accuracy, by a quantum state with a regular Glauber-Sudarshan P function. We propose applications of our results for estimating the output state of an unknown quantum process and estimating the outcome probabilities of quantum measurements.

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Phys. Rev. A 107, 053706– Published 10 May, 2023
  • Received 4 July 2022
  • Revised 10 January 2023
  • Accepted 24 April 2023
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