Exchange-Symmetrized Qudit Bell Bases and Bell-State Distinguishability

TL;DR

This paper introduces a new exchange-symmetrized Bell basis for even-dimensional qudits, demonstrating that up to 2d-1 Bell states can be distinguished with linear evolution and local measurement, reaching the theoretical limit.

Contribution

It generalizes exchange-symmetrized Bell bases to arbitrary even dimensions and establishes the maximum number of Bell states distinguishable by LELM for these systems.

Findings

Maximum of 2d-1 Bell states distinguishable with LELM for even d

Complete exchange-symmetrized basis cannot exist for odd d

Extends prior work on hyperentangled qubit bases to higher dimensions

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 two. 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 $d = 2^n$ and $d=3$. This result is relevant to near-term realizations of quantum communication protocols.