Optimal unambiguous discrimination of Bell-like states with linear optics

Dov Fields, János A. Bergou, Mark Hillery, Siddhartha Santra, and Vladimir S. Malinovsky
Phys. Rev. A 106, 023706 – Published 8 August 2022

Abstract

Quantum information processing using linear optics is challenging due to the limited set of deterministic operations achievable without using complicated resource-intensive methods. While techniques such as the use of ancillary photons can enhance the information processing capabilities of linear optical systems, they are technologically demanding. Therefore, determining the constraints posed by linear optics and optimizing linear optical operations for specific tasks under those constraints, without the use of ancillae, can facilitate their potential implementation. Here, we consider the task of unambiguously discriminating between Bell-like states using linear optics and without the use of ancillary photons. This is a basic problem relevant in diverse settings, for example, in the measurement of the output of an entangling quantum circuit or for entanglement swapping at a quantum repeater station. While it is known that exact Bell states of two qubits can be discriminated with an optimal success probability of 50%, we find, surprisingly, that for Bell-like states the optimal probability can be only 25%. We analyze a set of Bell-like states in terms of their distinguishability, entanglement as measured by concurrence, and parameters of the beam-splitter network used for unambiguous discrimination. Further, we provide the linear optical configuration comprising single-photon detectors and beam splitters with input-state-dependent parameters that achieves optimal discrimination in the Bell-like case.

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  • Received 7 December 2021
  • Revised 7 July 2022
  • Accepted 25 July 2022

DOI:https://doi.org/10.1103/PhysRevA.106.023706

©2022 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Dov Fields1, János A. Bergou2,3, Mark Hillery2,3, Siddhartha Santra1,4, and Vladimir S. Malinovsky1

  • 1DEVCOM Army Research Laboratory, Adelphi, Maryland 20783, USA
  • 2Department of Physics and Astronomy, Hunter College of the City University of New York, New York, New York 10065, USA
  • 3Graduate Center of the City University of New York, New York, New York 10016, USA
  • 4Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

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Issue

Vol. 106, Iss. 2 — August 2022

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