Exchange-Symmetrized Qudit Bell Bases and Bell-State Distinguishability
arXiv:2412.10297 · doi:10.1103/vdb2-t7bz
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 two. For our exchange-symmetrized basis we show that measurement devices restricted to linear evolution and local measurement (LELM) can unambiguously distinguish 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 and . This result is relevant to near-term realizations of quantum communication protocols.
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