Construction of genuinely entangled multipartite subspaces from bipartite ones by reducing the total number of separated parties

Antipin, K. V.

doi:10.1016/j.physleta.2022.128248

Cited by 4 publications

(4 citation statements)

References 52 publications

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“…We have checked numerically that is not true for the nUPBs from Proposition 4 with some chosen nodes for low dimensional small systems, but we have not been able to verify whether this holds in general for the given subspaces. A somewhat complementary question is whether our approach allows for a construction of fully nonpositive partial transpose (NPT) GESs, that is GESs that support only states being NPT across all bipartitions [9,23], and in case of a positive answer which dimensions of GESs could be achieved. This is especially intriguing in view of the recent construction of large fully NPT stabilizer GESs [21].…”

Section: Gme Mixed Statesmentioning

confidence: 99%

“…[7] was based on unextendible product bases (UPBs) [15,16] a natural notion for constructing entangled sub-Maciej Demianowicz: maciej.demianowicz@pg.edu.pl spaces -specifically, their nonorthogonal variant (nUPBs) [17]. Further developments made use of various tools and concepts: unextendible biproduct bases [9], certain characterization of bipartite completely entangled subspaces [18], stabilizer formalism [19,20,21], correspondence between quantum channels and subspaces of tensor product Hilbert spaces [22], or compositional (tensor product) approach [23]. While some of these proposal [18,22] offer the possibility of constructing GESs of any sizes, their actual general utility is only theoretical as they do not provide a recipe to achieve this task in any multipartite scenario and their applicability is in fact very limited and boils down to small systems.…”

Section: Introductionmentioning

confidence: 99%

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Universal construction of genuinely entangled subspaces of any size

Demianowicz

2022

Quantum

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We put forward a simple construction of genuinely entangled subspaces – subspaces supporting only genuinely multipartite entangled states – of any permissible dimensionality for any number of parties and local dimensions. The method uses nonorthogonal product bases, which are built from totally nonsingular matrices with a certain structure. We give an explicit basis for the constructed subspaces. An immediate consequence of our result is the possibility of constructing in the general multiparty scenario genuinely multiparty entangled mixed states with ranks up to the maximal dimension of a genuinely entangled subspace.

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Section: Gme Mixed Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Universal construction of genuinely entangled subspaces of any size

Demianowicz

2022

Quantum

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“…After finding several examples of CES subspaces the interest in studying a special type of CES, that is genuinely entangled subspaces (GES) [15][16][17][18][19][20][21] has gained some attention. These GESs contain only states which are genuinely entangled.…”

Section: Introductionmentioning

confidence: 99%

“…Afterwards, a method based on the correspondence between bipartite entangled subspaces and certain quantum channels has been presented in [20] to construct GESs subspaces. A more recent approach has been given in [21] in which a multipartite GESs can be constructed using an arbitrary collection of bipartite GESs by joining their adjacent subsystems under certain conditions.…”

Section: Introductionmentioning

confidence: 99%

Completely entangled subspaces from Moore-like matrices

Nawareg

2023

Phys. Scr.

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Construction of completely entangled subspaces (CES) has gained a considerable attention, recently. These subspaces which contain only entangled states are of great importance for entanglement theory and also provide a valuable resource for quantum information processing tasks. The results of [Proc. Math. Sci. 114, 365 (2004)] and in particular using the properties of certain matrix, namely Vandermonde matrix, to build CES motivated us to search for new distinct CES’s. Mainly, the stimulating question of whether there are other matrices that can lead to building CESs emerged. In the current paper we give an affirmative answer to this question by providing a method for constructing CESs using the properties of Moore-like matrices. In addition, we give few examples for the proposed subspaces in case of 3-qubit and 2-qutrit systems. Then a comparison between the resulted subspaces and those constructed from Vandermonde matrix has been given for the systems understudy. The results shows that the two methods give identically the same subspaces in case of multiqubit systems. However, for multipartite systems with local dimensions d ≥ 3 the two methods gave unequivalent CES subspaces. Interestingly, the properties of the proposed Moore-like matrices provided a far rich way for constructing CES subspaces. It leads to generating as many distinct CES’s as we want for each multipartite quantum system. This is in contrary to Vandermonde-based method which can give only one CES per system. In addition, the basis for each of the given examples has been obtained in a simple form. Moreover, we evaluated the entanglement of uniformly mixed states over the obtained subspaces in terms of concurrence and geometric measure of entanglement. Since different parameters of a Moore-like matrix lead to distinct CESs for the same system, the realized results can open the door for more investigations and/or applications.

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Negative result about the construction of genuinely entangled subspaces from unextendible product bases

Demianowicz

2022

Phys. Rev. A

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Construction of genuinely entangled multipartite subspaces from bipartite ones by reducing the total number of separated parties

Cited by 4 publications

References 52 publications

Universal construction of genuinely entangled subspaces of any size

Universal construction of genuinely entangled subspaces of any size

Completely entangled subspaces from Moore-like matrices

Negative result about the construction of genuinely entangled subspaces from unextendible product bases

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