Dimension-Free Entanglement Detection in Multipartite Werner States

Huber, Felix; Klep, Igor; Magron, Victor; Volčič, Jurij

doi:10.1007/s00220-022-04485-9

Cited by 7 publications

(4 citation statements)

References 44 publications

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“…Consequently, to improve the algorithm further we have included mixed entangled states in our training model. For instance, let us consider another important family of multipartite quantum states ˆ W , so called Werner states [46,47], which involve entanglement of mixed states.…”

Section: B Constructing Entanglement Witness Operators Via Linear Sup...mentioning

confidence: 99%

Classification of four-qubit entangled states via machine learning

et al. 2023

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We apply the support vector machine (SVM) algorithm to derive a set of entanglement witnesses (EW) to identify entanglement patterns in families of four-qubit states. The effectiveness of SVM for practical EW implementations stems from the coarse-grained description of families of equivalent entangled quantum states. The equivalence criteria in our work is based on the stochastic local operations and classical communication (SLOCC) classification and the description of the fourqubit entangled Werner states. We numerically verify that the SVM approach provides an effective tool to address the entanglement witness problem when the coarse-grained description of a given family state is available. We also discuss and demonstrate the efficiency of nonlinear kernel SVM methods as applied to four-qubit entangled state classification.

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Section: B Constructing Entanglement Witness Operators Via Linear Sup...mentioning

confidence: 99%

Classification of four-qubit entangled states via machine learning

et al. 2023

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“…Recently a one-to-one correspondence between inequalities for matrix trace polynomials and Werner state witnesses was established [13]. One the one hand, the formalism opened the way to perform dimension-free entanglement detection, a method that is independent of the local Hilbert space dimension [14]. On the other hand, it offers a systematic computational method to prove matrix inequalities from the positive cone, thus complementing methods from algebraic geometry.…”

Section: Introductionmentioning

confidence: 99%

Positive maps from the walled Brauer algebra

Balanzó-Juandó,

Studziński,

Huber

2024

J. Phys. A: Math. Theor.

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We present positive maps and matrix inequalities for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps that are in one-to-one correspondence with elements fromthe walled Brauer algebra. Using our formalism, these maps can be obtained in a systematic and clear way by manipulating partially transposed permutation operators under a partial trace. Additionally, these maps are reasonably easy in construction by combining an algorithmic approach with graphical calculus.

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“…Here, the study of unitary invariance has some tradition. 1,2,26,27 Consider the two-qubit singlet state…”

Section: Introductionmentioning

confidence: 99%

Multiparticle singlet states cannot be maximally entangled for the bipartitions

Bernards,

Gühne

2024

Journal of Mathematical Physics

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One way to explore multiparticle entanglement is to ask for maximal entanglement with respect to different bipartitions, leading to the notion of absolutely maximally entangled states or perfect tensors. A different path uses unitary invariance and symmetries, resulting in the concept of multiparticle singlet states. We show that these two concepts are incompatible in the sense that the space of pure multiparticle singlet states does not contain any state for which all partitions of two particles vs the rest are maximally entangled. This puts restrictions on the construction of quantum codes and contributes to discussions in the context of the anti-de Sitter/conformal field theory correspondence and quantum gravity.

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Dimension-Free Entanglement Detection in Multipartite Werner States

Cited by 7 publications

References 44 publications

Classification of four-qubit entangled states via machine learning

Classification of four-qubit entangled states via machine learning

Positive maps from the walled Brauer algebra

Multiparticle singlet states cannot be maximally entangled for the bipartitions

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