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  • Open Access

Exchange-symmetrized qudit Bell bases and Bell-state distinguishability

Oscar Scholin*

Theresa W. Lynn†

  • Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom and Department of Physics, Pomona College, 610 N. College Avenue, Claremont, California 91711, USA

  • Department of Physics, Harvey Mudd College, 301 Platt Boulevard, Claremont, California 91711, USA

  • *Contact author: orsa2020@mymail.pomona.edu
  • †Contact author: lynn@hmc.edu
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Phys. Rev. Research 7, 033124 – Published 6 August, 2025

DOI: https://doi.org/10.1103/vdb2-t7bz

Abstract

Entanglement of qudit pairs, with single-particle Hilbert space dimension d, has important potential for quantum information processing, with applications in cryptography, algorithms, and error correction. For a pair of qudits of arbitrary even dimension d, we introduce a generalized Bell basis with definite symmetry under exchange of internal states between the two particles. We show that no complete exchange-symmetrized basis can exist for odd d. This framework extends prior work on exchange-symmetrized hyperentangled qubit bases, where d is a power of 2. For our exchange-symmetrized basis, we show that measurement devices restricted to linear evolution and local measurement (LELM) can unambiguously distinguish 2d−1 qudit Bell states for any even d. This achieves the upper bound in general for reliable Bell-state distinguishability via LELM and augments previously known limits for d=2n and d=3. This result is relevant to near-term realizations of quantum communication protocols.

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Phys. Rev. Research 7, 033124– Published 6 August, 2025
  • Received 18 December 2024
  • Accepted 14 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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