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arXiv · 2412.10297

Exchange-Symmetrized Qudit Bell Bases and Bell-State Distinguishability

Oscar Scholin·Theresa W. Lynn
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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.

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Oscar Scholin, Theresa W. Lynn. 2024-12-13. Exchange-Symmetrized Qudit Bell Bases and Bell-State Distinguishability. https://doi.org/10.1103/vdb2-t7bz

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