Qudits offer no advantages over dits for sending random messages
Quantum Physics
2025-12-03 v1 Information Theory
math.IT
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.
Cite
@article{arxiv.2512.02477,
title = {Qudits offer no advantages over dits for sending random messages},
author = {Ronit Shah},
journal= {arXiv preprint arXiv:2512.02477},
year = {2025}
}