Exchange-symmetrized qudit Bell bases and Bell-state distinguishability

Oscar Scholin and Theresa W. Lynn*

Physical Review Research 7, 033124 (2025)

Abstract

Entanglement of qudit pairs, with single-particle Hilbert space dimension , has important potential for quantum information processing, with applications in cryptography, algorithms, and error correction. For a pair of qudits of arbitrary even dimension , 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 . This framework extends prior work on exchange-symmetrized hyperentangled qubit bases, where 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 2⁢ −1 qudit Bell states for any even . This achieves the upper bound in general for reliable Bell-state distinguishability via LELM and augments previously known limits for =2 and =3. This result is relevant to near-term realizations of quantum communication protocols.