Compatibility of subsystem states and convex geometry

Hall, W. B.

doi:10.1103/physreva.75.032102

Cited by 26 publications

(25 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As remarked, the question of joinability has been extensively investigated in the context of the classical [31] and quantum [9,23,32,33] marginal problem. A joining state is equivalenty referred to as an extension or an element of the pre-image of the list under the reduction map, while the members of a list of joinable states are also said to be compatible or consistent.…”

Section: A Joinabilitymentioning

confidence: 99%

Compatible quantum correlations: Extension problems for Werner and isotropic states

Johnson

Viola

2013

Phys. Rev. A

View full text Add to dashboard Cite

We investigate some basic scenarios in which a given set of bipartite quantum states may consistently arise as the set of reduced states of a global N -partite quantum state. Intuitively, we say that the multipartite state "joins" the underlying correlations. Determining whether, for a given set of states and a given joining structure, a compatible N -partite quantum state exists is known as the quantum marginal problem. We restrict to bipartite reduced states that belong to the paradigmatic classes of Werner and isotropic states in d dimensions, and focus on two specific versions of the quantum marginal problem which we find to be tractable. The first is Alice-Bob, Alice-Charlie joining, with both pairs being in a Werner or isotropic state. The second is m-n sharability of a Werner state across N subsystems, which may be seen as a variant of the N -representability problem to the case where subsystems are partitioned into two groupings of m and n parties, respectively. By exploiting the symmetry properties that each class of states enjoys, we determine necessary and sufficient conditions for three-party joinability and 1-n sharability for arbitrary d. Our results explicitly show that although entanglement is required for sharing limitations to emerge, correlations beyond entanglement generally suffice to restrict joinability, and not all unentangled states necessarily obey the same limitations. The relationship between joinability and quantum cloning as well as implications for the joinability of arbitrary bipartite states are discussed.

show abstract

Section: A Joinabilitymentioning

confidence: 99%

Compatible quantum correlations: Extension problems for Werner and isotropic states

Johnson

Viola

2013

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…While it is straightforward to check whether some reduced states are compatible with a given global state, the question becomes much subtler when the global state is unknown and one is interested in knowing whether there exists a quantum state compatible with the given marginals. Finding the conditions for compatibility among reduced quantum states is known as the quantum marginal problem [3][4][5][6]. It is the quantum counterpart of the classical marginal problem, which is concerned with the compatibility of marginal probability distributions.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal multipartite correlations from local marginal probabilities

et al. 2012

View full text Add to dashboard Cite

Understanding what can be inferred about a multiparticle quantum system given only the knowledge of its subparts is a highly nontrivial task. Clearly, if a global system does not contain an information resource of some kind, neither do its subparts. For the case of entanglement as an information resource, it is known that the converse of this last statement is not true: Some nonentangled reduced states are only compatible with global states which are entangled. We extend this result to correlations and provide local marginal correlations that are only compatible with global genuinely tripartite nonlocal correlations. Quantum nonlocality can thus be deduced from the mere observation of local marginal correlations.

show abstract

“…Possible extensions of the present framework include applications to state reconstruction from local marginals and its connection to entanglement generation [27], [28], as well as comparison with the existing approximate results [21] in physically meaningful situation. Lastly, the advantage offered by the introduction of an a priori state in the estimation problem can be exploited to devise recursive algorithms, that update existing estimate in an optimal way relying only on partial data.…”

Section: Discussionmentioning

confidence: 98%

Minimum Relative Entropy for Quantum Estimation: Feasibility and General Solution

Zorzi

Ticozzi

Ferrante

2014

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data, find the maximal common kernel of all admissible states and, whenever necessary, to relax the constraints in order to allow for a physically admissible solution. Building on these results, the variational analysis can be completed ensuring existence and uniqueness of the optimum. The latter can then be computed by standard, efficient standard algorithms for convex optimization, without resorting to approximate methods or restrictive assumptions on its rank

show abstract

Compatibility of subsystem states and convex geometry

Cited by 26 publications

References 28 publications

Compatible quantum correlations: Extension problems for Werner and isotropic states

Compatible quantum correlations: Extension problems for Werner and isotropic states

Nonlocal multipartite correlations from local marginal probabilities

Minimum Relative Entropy for Quantum Estimation: Feasibility and General Solution

Contact Info

Product

Resources

About