Ronit Shah | Searcharxiv

arXiv2025

Qudits offer no advantages over dits for sending random messages

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.

quant-ph↗

arXiv2025

A Faster Quantum Fourier Transform

We present an asymptotically improved algorithm for implementing the Quantum Fourier Transform (QFT) in both the exact and approximate settings. Historically, the approximate QFT has been implemented in $\Theta(n \log n)$ gates, and the exact in $\Theta(n^2)$ gates. In this work, we show that these costs can be reduced by leveraging a novel formulation of the QFT that recurses on two partitions of the qubits. Specifically, our approach yields an $\Theta(n(\log \log n)^2)$ algorithm for the approximate QFT using $\Theta(\log n)$ ancillas, and an $\Theta(n(\log n)^2)$ algorithm for the exact QFT requiring $\Theta(n)$ ancillas.

quant-ph↗