Simultaneous Estimation of Nonlinear Functionals of a Quantum State

IEEE Transactions on Information Theory 2026 Open access

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Authors: Kean Chen, Qisheng Wang, Yu Zhan, Zhicheng Zhang
DOI: 10.1109/tit.2026.3699531
Cited by: 0

Abstract

We consider a fundamental task in quantum information theory, estimating the values of tr(Oρ), tr(Oρ2), . . . , tr(Oρk) for an observableOand a quantum state ρ. We show that Θ(k) samples of ρ are sufficient and necessary to simultaneously estimate all thekvalues. This means that estimating all thekvalues is almost as easy as estimating only one of them, tr(Oρk). As an application, our approach advances the sample complexity of entanglement spectroscopy and the virtual cooling for quantum many-body systems. Moreover, we extend our approach to estimating general functionals by polynomial approximation.

Fields of Study & Subjects

Quantum Computing Algorithms and Architecture Quantum many-body systems Quantum Information and Cryptography

Publication details

Journal / source
IEEE Transactions on Information Theory
Volume
72
Issue
9
Pages
6740–6751
Publication date
4 June 2026
Language
EN