Correlation-based entanglement criterion in bipartite multiboson systems

Laskowski, Wiesław; Markiewicz, Marcin; Rosseau, Danny; Byrnes, Tim; Kostrzewa, Kamil; Kołodziejski, Adrian

doi:10.1103/physreva.92.022339

Cited by 6 publications

(8 citation statements)

References 51 publications

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“…The consequences of Definition 5 have been sudied by several authors [155,156,120,157,158,159,160,161,162,163,164,165,166], and applied in particular to condensed matter systems [167,168,169,170,171] The motivation for this formulation of particle-entanglement originates from a rather specific physical setting requiring information transmission from a system of identical particles to a quantum register made of distinguishable qubits, usually described by tensor products of single-particle Hilbert spaces with fixed numbers of particles in suitably chosen subgroups. This condition on one hand confirms that the locality criterion underlying entanglement-III is also related to the particle picture as in Definition 2 and, on the other hand, that it can be implemented by selecting degrees of freedom and corresponding observables associated with the confinement of individual particle states to orthogonal subspaces, say V 1 and V 2 , of the single-particle Hilbert space.…”

Section: Definition 5 (Entanglement-iiimentioning

confidence: 99%

Entanglement in indistinguishable particle systems

et al. 2020

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For systems consisting of distinguishable particles, there exists an agreed upon notion of entanglement which is fundamentally based on the possibility of addressing individually each one of the constituent parties. Instead, the indistinguishability of identical particles hinders their individual addressability and has prompted diverse, sometimes discordant definitions of entanglement. In the present review, we provide a comparative analysis of the relevant existing approaches, which is based on the characterization of bipartite entanglement in terms of the behaviour of correlation functions. Such a a point of view provides a fairly general setting where to discuss the presence of non-local effects; it is performed in the light of the following general consistency criteria: i) entanglement corresponds to non-local correlations and cannot be generated by local operations; ii) when, by "freezing" suitable degrees of freedom, identical particles can be effectively distinguished, their entanglement must reduce to the one that holds for distinguishable particles; iii) in absence of other quantum resources, only entanglement can outperform classical information protocols. These three requests provide a setting that allows to evaluate strengths and weaknesses of the existing approaches to indistinguishable particle entanglement and to contribute to the current understanding of such a crucial issue. Indeed, they can be classified into five different classes: four hinging on the notion of particle and one based on that of physical modes. We show that only the latter approach is consistent with all three criteria, each of the others indeed violating at least one of them.

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Section: Definition 5 (Entanglement-iiimentioning

confidence: 99%

Entanglement in indistinguishable particle systems

et al. 2020

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“…In this section we will use the introduced formalism for a reconsideration of the so called geometrical criteria for entanglement introduced in [13] and further developed in a series of works [8][9][10][11][12]. All the criteria of this type are based on an entanglement identifier (7) generated by the map G which is linear (34) and which fulfills the following condition:…”

Section: A Linear Geometrical Entanglement Criteriamentioning

confidence: 99%

“…There has been an attempt to generalize this approach for detection of genuine multipartite entanglement [4][5][6][7], however no general construction of such criteria, which would be optimal for arbitrary state exists. The second group of entanglement indicators involves so called geometric criteria [8][9][10][11][12], which in the simplest bipartite case read [13]:…”

Section: Introductionmentioning

confidence: 99%

Unified approach to geometric and positive-map-based nonlinear entanglement identifiers

et al. 2018

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Detecting quantumness of correlations (especially entanglement) is a very hard task even in the simplest case i.e. two-partite quantum systems. Here we provide an analysis whether there exists a relation between two most popular types of entanglement identifiers: the first one based on positive maps and not directly applicable in laboratory and the second one -geometric entanglement identifier which is based on specific Hermiticity-preserving maps. We show a profound relation between those two types of entanglement criteria. Hereunder we have proposed a general framework of nonlinear functional entanglement identifiers which allows us to construct new experimentally friendly entanglement criteria.

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“…In order to check the entanglement condition (2), we put the correlation tensor of a state (5) in a Schmidt form itself. The general form of the tensor elements is given in Appendix C. Note that the Schmidt form of the state (5) does not imply a diagonal form of the corresponding tensor. Even for a two-qutrit state non-diagonal elements appear.…”

Section: Basic Aimsmentioning

confidence: 99%

“…In this section, we analyze noise resistance of violation of Bell-type inequalities for the bipartite quantum states (5). To this end, we employ the CGLMP inequality in- troduced in Ref.…”

Section: Testing Entanglement With Bell Inequalitiesmentioning

confidence: 99%

Entanglement criteria for noise resistance of two-qudit states

et al. 2016

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Too much noise kills entanglement. This is the main problem in its production and transmission. We use a handy approach to indicate noise resistance of entanglement of a bi-partite system described by d × d Hilbert space. Our analysis uses a geometric approach based on the fact that if a scalar product of a vector s with a vector e is less than the square of the norm of e, then s = e. We use such concepts for correlation tensors of separable and entangled states. As a general form correlation tensors for pairs of qudits, for d > 2, is very difficult to obtain, because one does not have a Bloch sphere for pure one qudit states, we use a simplified approach. The criterion reads: if the largest Schmidt eigenvalue of a correlation tensor is smaller than the square of its norm, then the state is entangled. this criterion is applied in the case of various types of noise admixtures to the initial (pure) state. These include white noise, colored noise, local depolarizing noise and amplitude damping noise. A broad set of numerical and analytical results is presented. As the other simple criterion for entanglement is violation of Bell's inequalities, we also find critical noise parameters to violate specific family of Bell inequalities (CGLMP), for maximally entangled states. We give analytical forms of our results for d approaching infinity.

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Correlation-based entanglement criterion in bipartite multiboson systems

Cited by 6 publications

References 51 publications

Entanglement in indistinguishable particle systems

Entanglement in indistinguishable particle systems

Unified approach to geometric and positive-map-based nonlinear entanglement identifiers

Entanglement criteria for noise resistance of two-qudit states

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