# Gaussian Quantum Marginal Problem

@article{Eisert2008GaussianQM, title={Gaussian Quantum Marginal Problem}, author={Jens Eisert and Tom{\'a}{\vs} Tyc and Terry Rudolph and Barry C. Sanders}, journal={Communications in Mathematical Physics}, year={2008}, volume={280}, pages={263-280} }

The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our…

## 34 Citations

A complete hierarchy for the pure state marginal problem in quantum mechanics

- Computer ScienceNature communications
- 2021

This paper proves a correspondence of the marginal problem to the separability problem, and describes a sequence of semidefinite programs which can decide whether some given marginals are compatible with some pure global quantum state.

Gaussian entanglement revisited

- Computer Science
- 2016

We present a novel approach to the separability problem for Gaussian quantum states of bosonic continuous variable systems. We derive a simplified necessary and sufficient separability criterion for…

Eigenvalue Distributions of Reduced Density Matrices

- Mathematics
- 2014

Given a random quantum state of multiple distinguishable or indistinguishable particles, we provide an effective method, rooted in symplectic geometry, to compute the joint probability distribution…

Inequalities for quantum marginal problems with continuous variables

- Mathematics
- 2014

We consider a mixed continuous-variable bosonic quantum system and present inequalities which must be satisfied between principal values of the covariances of a complete set of observables of the…

Extendibility of Bosonic Gaussian States.

- Computer SciencePhysical review letters
- 2019

A simple semidefinite program is derived, whose size scales linearly with the number of local modes, to efficiently decide k-extendibility of any given bosonic Gaussian state.

Quantum marginal problems

- Physics
- 2015

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…

Quantum thermodynamics in a multipartite setting: A resource theory of local Gaussian work extraction for multimode bosonic systems

- MathematicsPhysical Review A
- 2019

Quantum thermodynamics can be cast as a resource theory by considering free access to a heat bath, thereby viewing the Gibbs state at a fixed temperature as a free state and hence any other state as…

Constraints on Multipartite Quantum Entropies

- PhysicsArXiv
- 2018

This thesis improves on previously known results by showing that under a technical condition on the localdimension, entropies of stabilizer states respect an additional class of information inequalities that isvalid for random variables from linear codes.

Classical analog of the quantum marginal problem

- Computer Science, Physics
- 2020

A classical cryptographic analog of multipartite entanglement which can be verified solely from separable marginals is constructed, demonstrating that the emergent correlation properties do not exist only in the quantum world.

Hawking radiation and the quantum marginal problem

- PhysicsJournal of Cosmology and Astroparticle Physics
- 2022

In 1974 Steven Hawking showed that black holes emit thermal radiation, which eventually causes them to evaporate. The problem of the fate of information in this process is known as the “black hole…

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