Classifying quantum entanglement through topological links

Quinta, Gonçalo M.; André, Rui

doi:10.1103/physreva.97.042307

Cited by 11 publications

(25 citation statements)

References 12 publications

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“…To prove this statement we use the technique of associating rings to polynomials provided in [30]. Consider a polynomial of N variables, P m (x 1 , x 2 , .…”

Section: Discussionmentioning

confidence: 99%

“…These rules for polynomial construction can then be used to count the number of distinct ways to link a given number of rings. For N = 2, 3, 4 and 5 rings, there are respectively 1, 4, 40 and 6900 ways to form a link [30], while for an arbitrary N the corresponding number has not been found yet. A particularly interesting subclass of links with N rings is one where all rings remain connected after any m < N cuts, but become fully separated if m + 1 cuts are performed.…”

Section: ) Relabeling Of Variables Is Irrelevant;mentioning

confidence: 98%

“…We use the notation n i , introduced in [30], where n is the number of rings and i is a cataloging index denoting the specific link class. Eq.…”

Section: M-resistant Linksmentioning

confidence: 99%

“…with |ψ 4,m specified case by case. It is also worth mentioning that the links for more than three rings have been drawn using a technique developed in [30] that makes direct use of the polynomials associated with them. For m = 0, the corresponding monomial reads…”

Section: N =3mentioning

confidence: 99%

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Cut-resistant links and multipartite entanglement resistant to particle loss

Quinta¹,

André²,

Burchardt³

et al. 2019

Phys. Rev. A

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In this work, we explore the space of quantum states composed of N particles. To investigate the entanglement resistant to particles loss, we introduce the notion of m-resistant states. A quantum state is m-resistant if it remains entangled after losing an arbitrary subset of m particles, but becomes separable after losing a number of particles larger than m. We establish an analogy to the problem of designing a topological link consisting of N rings such that, after cutting any (m + 1) of them, the remaining rings become disconnected. We present a constructive solution to this problem, which allows us to exhibit several distinguished N -particles states with the desired property of entanglement resistance to a particle loss.

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“…To prove this statement we use the technique of associating rings to polynomials provided in [30]. Consider a polynomial of N variables, P m (x 1 , x 2 , .…”

Section: Discussionmentioning

confidence: 99%

Section: ) Relabeling Of Variables Is Irrelevant;mentioning

confidence: 98%

“…We use the notation n i , introduced in [30], where n is the number of rings and i is a cataloging index denoting the specific link class. Eq.…”

Section: M-resistant Linksmentioning

confidence: 99%

Section: N =3mentioning

confidence: 99%

See 2 more Smart Citations

Cut-resistant links and multipartite entanglement resistant to particle loss

Quinta¹,

André²,

Burchardt³

et al. 2019

Phys. Rev. A

Self Cite

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show abstract

“…of distorted black holes [19,20], in the spacetimes of dimension higher (or smaller) than 4 [21][22][23][24][25][26][27][28][29][30][31].…”

mentioning

confidence: 99%

Vacuum Polarization of Massive Fields in the Spacetime of the Higher-dimensional Black Holes

Matyjasek¹,

Tryniecki²

2018

Acta Phys. Pol. B

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We construct and study the vacuum polarization, φ 2 D , of the quantized massive scalar field with a general curvature coupling parameter in higher-dimensional static and spherically-symmetric black hole spacetimes, with a special emphasis put on the electrically charged Tangherlini solutions and the extremal and ultraextremal configurations. For 4 ≤ D ≤ 7 the explicit analytic expressions for the vacuum polarization are given. For the conformally coupled fields the relation between the trace of the stress-energy tensor and the vacuum polarization is examined, which requires knowledge of the higher-order terms in the Schwinger-DeWitt expansion.

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Coarse-grained entanglement classification through orthogonal arrays

Seveso

Goyeneche

Życzkowski

2018

Journal of Mathematical Physics

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Classification of entanglement in multipartite quantum systems is an open problemsolved so far only for bipartite systems and for systems composed of three and four qubits. We propose here a coarse-grained classification of entanglement in systems consisting of N subsystems with an arbitrary number of internal levels each, based on properties of orthogonal arrays with N columns. In particular, we investigate in detail a subset of highly entangled pure states which contains all states defining maximum distance separable codes. To illustrate the methods presented, we analyze systems of four and five qubits, as well as heterogeneous tripartite systems consisting of two qubits and one qutrit or one qubit and two qutrits. I. INTRODUCTIONCharacterization of entanglement in multipartite systems has proven particularly challenging, even for pure states. As one moves from a bipartite to a multipartite scenario involving N parties, the algebraic structure becomes much richer. A pure multipartite quantum state is de-arXiv:1709.05916v4 [math.CO] 28 Jun 2018 := max I:|I|=t J t (I), where |I| denotes the cardinality of the multi-index I. Then, the generalized resolution is defined as(2) Clearly, t < GR < t+1. For two-level OAs, the above quantity is invariant under isomorphisms.However, for multi-level arrays, permutations of symbols within columns can change quantity 2) [23]. Hence the generalized resolution of a multi-level OA is defined as the maximum value of (2) taken over the family of all isomorphic arrays.

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Classifying quantum entanglement through topological links

Cited by 11 publications

References 12 publications

Cut-resistant links and multipartite entanglement resistant to particle loss

Cut-resistant links and multipartite entanglement resistant to particle loss

Vacuum Polarization of Massive Fields in the Spacetime of the Higher-dimensional Black Holes

Coarse-grained entanglement classification through orthogonal arrays

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