Entanglement marginal problems

Navascués, Miguel; Baccari, F.; Acín, Antonio

doi:10.22331/q-2021-11-25-589

Cited by 15 publications

(18 citation statements)

References 35 publications

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“…For example, a resource theory can be defined for the usual quantum states marginal problems, an incompatibility problem can be defined for the resource theory of entanglement, and so on. In particular, since a resource theory of entanglement-free incompatibility can be defined in relation to the recently introduced entanglement marginal problems [6], our robustness measure, etc., can be applied to this incompatibility. More generally, if a resource theory or a marginal problem can be cast in a form that fits our framework, results that we have derived are readily applicable.…”

Section: Discussionmentioning

confidence: 99%

“…Note that one may also choose 𝑅 = genuinely multipartite entanglement, which means that F 𝑅 is the convex hull of the union of all biseparable states. Then, as with the original entanglement marginal problems [6], marginal states that are only compatible with a genuinely multipartite entangled global state can be treated as a resource, and our framework immediately provides the corresponding resource theory, resource monotone, and its operational interpretation in terms of a subchannel discrimination task.…”

Section: Resource Theory Associated With the Entanglement Marginal Pr...mentioning

confidence: 93%

“…As a third example, consider the case of T = S and F 𝑅 = the set of fully separable states in some given multipartite system S. For σ 𝚲 ∈ ℭ 𝚲 , this gives exactly the entanglement marginal problem recently proposed in [6], which aim to characterize when a given set of marginal density matrices σ 𝚲 necessarily implies that the multipartite global state is entangled. By definition, all such entanglement-implying σ 𝚲 are 𝑅-free incompatible in the global system S.…”

Section: Resource Theory Associated With the Entanglement Marginal Pr...mentioning

confidence: 99%

“…A more refined version of such problems, which further demands that the global state is entangled, was comprehensively discussed in the recent work of Ref. [6] (see also [7,8]).…”

Section: Introductionmentioning

confidence: 99%

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Resource Marginal Problems

Hsieh¹,

Tabia²,

Yin³

et al. 2022

Preprint

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We introduce the resource marginal problems, which concern the possibility of having a resource-free target subsystem compatible with a given collection of marginal density matrices. By identifying an appropriate choice of resource 𝑅 and target subsystem T, our problems reduce, respectively, to the well-known marginal problems for quantum states and the problem of determining if a given quantum system is a resource. More generally, we define a set of marginal states to be resource-free incompatible with a target subsystem T if all global states compatible with this set must result in a resourceful state in T. We show that this incompatibility induces a resource theory that can be quantified by a monotone. We derive necessary and sufficient conditions for this monotone to be a finite conic program and further show, via the corresponding witnesses, that resourcefree incompatibility is equivalent to an operational advantage in some subchannel discrimination task. Via our framework, a clear connection can be established between any marginal problem (that involves some notion of incompatibility) for quantum states and a resource theory for quantum states. In addition, the universality of our framework leads, for example, to an immediate, quantitative understanding of the incompatibility associated with the recently-proposed entanglement marginal problems. As further applications, we provide the first example showing a form of transitivity of nonlocality (steerability) for quantum states. We discuss also the analogous framework in the dynamical regime and establish a set of theoretical results that closely mirror those obtained for a resource theory for quantum states. Again, they allow us to recover a wide variety of results related to the studies of channel marginal problems, channel resource theories, etc.

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Section: Discussionmentioning

confidence: 99%

Section: Resource Theory Associated With the Entanglement Marginal Pr...mentioning

confidence: 93%

Section: Resource Theory Associated With the Entanglement Marginal Pr...mentioning

confidence: 99%

“…A more refined version of such problems, which further demands that the global state is entangled, was comprehensively discussed in the recent work of Ref. [6] (see also [7,8]).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Resource Marginal Problems

Hsieh¹,

Tabia²,

Yin³

et al. 2022

Preprint

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show abstract

“…On one hand, they point at an alternative approach towards experimental investigation of the remarkable concept of genuine multipartite entanglement verifiable from incomplete sets of separable marginals. On the other hand, they also stimulate theoretical questions concerning the existence of a Gaussian classical analog of the quantum marginal problem [43] or the extendibility of the entanglement marginal problem [44] to Gaussian case. On a more general level, our results contribute to the development of methods of detection of global properties of multipartite quantum systems from partial information.…”

Section: Discussionmentioning

confidence: 99%

Convicting emergent multipartite entanglement with evidence from a partially blind witness

Nordgren¹,

Leskovjanová²,

Provazník³

et al. 2021

Preprint

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Genuine multipartite entanglement underlies correlation experiments corroborating quantum mechanics and it is an expedient empowering many quantum technologies. One of many counterintuitive facets of genuine multipartite entanglement is its ability to exhibit an emergent character, that is, one can infer its presence in some multipartite states merely from a set of its separable marginals. Here, we show that the effect can be found also in the context of Gaussian states of bosonic systems. Specifically, we construct examples of multimode Gaussian states carrying genuine multipartite entanglement which can be verified solely from separable nearest-neighbour two-mode marginals. The key tool of our construction is a genuine multipartite entanglement witness acting only on some two-mode reductions of the global covariance matrix, which we find by a numerical solution of a semi-definite programme. We also propose an experimental scheme for preparation of the simplest three-mode state, which requires interference of three correlatively displaced squeezed beams on two beam splitters. Besides revealing the concept of emergent genuine multipartite entanglement in the Gaussian scenario and bringing it closer to experimentally testable form, our results pave the way to effective diagnostics methods of global properties of multipartite states without complete tomography.

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Classical Representability for Partial Boolean Structures in Quantum Mechanics

Budroni

2023

Trails in Modern Theoretical and Mathematical Physics

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Entanglement marginal problems

Cited by 15 publications

References 35 publications

Resource Marginal Problems

Resource Marginal Problems

Convicting emergent multipartite entanglement with evidence from a partially blind witness

Classical Representability for Partial Boolean Structures in Quantum Mechanics

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