Exchange-Symmetrized Qudit Bell Bases and Bell-State Distinguishability

Entanglement of qudit pairs, with single particle Hilbert space dimension d, have important potential for quantum information processing, with applications in cryptography, algorithms, and error correction. We introduce a generalized Bell basis for a pair of qudits of arbitrary even dimension d with definite symmetry under particle exchange, and 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 two. We discuss connections to symmetry-protected quantum computation and quantum secret sharing. As a direct application of our basis, we quantify the distinguishability of qudit Bell states by devices restricted to linear evolution and local measurement (LELM). We show that for any even d, at most 2d-1 states can be distinguished, extending prior known results for d = 2ⁿ and d=3.