Eur. Phys. J. D (2015) 69: 209
https://doi.org/10.1140/epjd/e2015-60191-7

Topical Review

Quantum marginal problems

¹ Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, Kotlrášká 2, 61137 Brno, Czech Republic
² Department of Computer Science, Faculty of Informatics, Masaryk University, Botanická 68a, 60200 Brno, Czech Republic

^a e-mail: 51635@mail.muni.cz

Received: 20 March 2015
Received in final form: 3 July 2015
Published online: 11 September 2015

Abstract

The quantum marginal problem asks the question if elements of a given set of quantum states can be reduced states of some joint quantum state. In this paper we present various versions of the quantum marginal problem along with their solutions in the order in which they were published. The review begins with simple finite-dimensional composite systems and ends with results of the Gaussian quantum marginal problem that apply to systems of harmonic oscillators (e.g. modes of the quantum electromagnetic field).