Continuous-variable quantum compressed sensing

Published

July 9, 2012

Author(s)

Yi-Kai Liu, Matthias Ohliger, Vincent Nesme, David Gross, Jens Eisert

Abstract

We introduce a novel method to faithfully reconstruct unknown quantum states that are approximately low-rank, using only a few measurement settings. The method is general enough to allow for measurements from a continuous family, and is also applicable to continuous-variable states. As a technical result, this work generalizes quantum compressed sensing to the situation where the measured observables are taken from a so-called tight frame (rather than an orthonormal basis) -- hence covering most realistic measurement scenarios. As an application, we discuss the reconstruction of quantum states of light from homodyne detection and other types of measurements, and we present simulations that show the advantage of the proposed compressed sensing technique over present methods. Finally, we introduce a method to construct a certificate which guarantees the success of the reconstruction with no assumption on the state, and we show how slightly more measurements give rise to "universal" state reconstruction that is highly robust to noise.

Citation

New Journal of Physics

Pub Type

Journals

Download Paper

Local Download

Keywords

quantum state tomography, compressed sensing, homodyne tomography

Citation

Liu, Y. , Ohliger, M. , Nesme, V. , Gross, D. and Eisert, J. (2012), Continuous-variable quantum compressed sensing, New Journal of Physics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=910987 (Accessed October 11, 2025)