The general marginal problem

1987 ◽  
pp. 77-367 ◽  
Author(s):  
J. Hoffmann-Jørgensen
Keyword(s):  
Marginal Problem

scholarly journals Jordan products of quantum channels and their compatibility

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Mark Girard ◽  
Martin Plávala ◽  
Jamie Sikora
Keyword(s):  
Quantum State ◽  
Sufficient Conditions ◽  
The Other ◽  
Independent Interest ◽  
Quantum Channels ◽  
Semidefinite Programs ◽  
Jordan Product ◽  
Marginal Problem ◽  
Jordan Products ◽  
Product Of Matrices

AbstractGiven two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.

scholarly journals A Possible Time-Dependent Generalization of the Bipartite Quantum Marginal Problem

2018 ◽  
Vol 39 (5) ◽  
pp. 422-437 ◽  
Author(s):  
Giuseppe Baio ◽  
Dariusz Chruściński ◽  
Antonino Messina
Keyword(s):  
Time Dependent ◽  
Marginal Problem

scholarly journals Entanglement marginal problems

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 589
Author(s):  
Miguel Navascués ◽  
Flavio Baccari ◽  
Antonio Acín
Keyword(s):  
Quantum State ◽  
System Size ◽  
Separable Extension ◽  
Translation Invariant ◽  
Time Space ◽  
Marginal Problem ◽  
Spatial Dimensions ◽  
A Chain ◽  
Reduced Density ◽  
Star Configuration

We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite programming relaxations of the set of quantum state marginals admitting a fully separable extension. We connect the completeness of each hierarchy to the resolution of an analog classical marginal problem and thus identify relevant experimental situations where the hierarchies are complete. For finitely many parties on a star configuration or a chain, we find that we can achieve an arbitrarily good approximation to the set of nearest-neighbour marginals of separable states with a time (space) complexity polynomial (linear) on the system size. Our results even extend to infinite systems, such as translation-invariant systems in 1D, as well as higher spatial dimensions with extra symmetries.

From a ‘Marginal Problem’ to the ‘Supreme International Jurisdiction’

2021 ◽  
pp. 137-175
Author(s):  
Rotem Giladi
Keyword(s):  
United Nations ◽  
Genocide Convention ◽  
International Court Of Justice ◽  
International Jurisdiction ◽  
Court Of Justice ◽  
Marginal Problem ◽  
International Court ◽  
The United Nations

The first of two chapters to explore the theme protection, chapter 4 records the range of conflicting attitudes displayed by Jacob Robinson and Shabtai Rosenne towards the Genocide Convention during its drafting, with regard to and following its ratification, and at the International Court of Justice advisory proceedings on the question of reservations to the Convention. The chapter describes their early disinterest in and indifference towards the Genocide Convention as a ‘marginal problem’ on the United Nations agenda, but also the circumstances under which they came to acknowledge and appropriate the Convention’s Jewish paternity, exploit the opportunities it presented while, in private, recording their hostility towards Raphael Lemkin, its progenitor, as well as their derision of the Convention’s promise to protect Jewish existence.

scholarly journals Gaussian Quantum Marginal Problem

2008 ◽  
Vol 280 (1) ◽  
pp. 263-280 ◽  
Author(s):  
Jens Eisert ◽  
Tomáš Tyc ◽  
Terry Rudolph ◽  
Barry C. Sanders
Keyword(s):  
Marginal Problem

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

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Xiao-Dong Yu ◽  
Timo Simnacher ◽  
Nikolai Wyderka ◽  
H. Chau Nguyen ◽  
Otfried Gühne
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Error Correcting Codes ◽  
Quantum Codes ◽  
Semidefinite Programs ◽  
Marginal Problem ◽  
Separability Problem ◽  
Pure Quantum State ◽  
Maximally Entangled States ◽  
Quantum Error

AbstractClarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state for some given marginals. This problem arises in many contexts, ranging from quantum chemistry to entanglement theory and quantum error correcting codes. In this paper, we prove a correspondence of the marginal problem to the separability problem. Based on this, we describe a sequence of semidefinite programs which can decide whether some given marginals are compatible with some pure global quantum state. As an application, we prove that the existence of multiparticle absolutely maximally entangled states for a given dimension is equivalent to the separability of an explicitly given two-party quantum state. Finally, we show that the existence of quantum codes with given parameters can also be interpreted as a marginal problem, hence, our complete hierarchy can also be used.

Sign in / Sign up

Export Citation Format

Share Document