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arXiv · 2512.02477

Qudits offer no advantages over dits for sending random messages

Ronit Shah
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Abstract

We consider the following simple scenario: Alice has one of many possible messages, drawn from a known distribution, and wants to maximize the probability that Bob guesses her message correctly. We prove that if Alice can send only a qudit to Bob, without preshared entanglement, there is never any advantage over sending him a classical dit. This result was previously known only for a uniform distribution. We also prove a mixed-state generalization of this result in the form of an upper bound on the success probability of discriminating between mixed quantum states with a single measurement. This bound is based solely on the dimension, probability distribution, and eigenvalues of the states and is sharp among such bounds.

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Ronit Shah. 2025-12-02. Qudits offer no advantages over dits for sending random messages. https://arxiv.org/abs/2512.02477

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