Near optimal quantum algorithm for estimating Shannon entropy

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Shin, Myeongjin, Jeong, Kabgyun
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866914297167216640
author Shin, Myeongjin
Jeong, Kabgyun
author_facet Shin, Myeongjin
Jeong, Kabgyun
contents We present a near-optimal quantum algorithm, up to logarithmic factors, for estimating the Shannon entropy in the quantum probability oracle model. Our approach combines the singular value separation algorithm with quantum amplitude amplification, followed by the application of quantum singular value transformation. On the lower bound side, we construct probability distributions encoded via Hamming weights in the oracle, establishing a tight query lower bound up to logarithmic factors. Consequently, our results show that the tight query complexity for estimating the Shannon entropy within $ε$-additive error is given by $\tildeΘ\left(\tfrac{\sqrt{n}}ε\right)$.
format Preprint
id arxiv_https___arxiv_org_abs_2509_07452
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Near optimal quantum algorithm for estimating Shannon entropy
Shin, Myeongjin
Jeong, Kabgyun
Quantum Physics
We present a near-optimal quantum algorithm, up to logarithmic factors, for estimating the Shannon entropy in the quantum probability oracle model. Our approach combines the singular value separation algorithm with quantum amplitude amplification, followed by the application of quantum singular value transformation. On the lower bound side, we construct probability distributions encoded via Hamming weights in the oracle, establishing a tight query lower bound up to logarithmic factors. Consequently, our results show that the tight query complexity for estimating the Shannon entropy within $ε$-additive error is given by $\tildeΘ\left(\tfrac{\sqrt{n}}ε\right)$.
title Near optimal quantum algorithm for estimating Shannon entropy
topic Quantum Physics
url https://arxiv.org/abs/2509.07452