Three-by-three bound entanglement with general unextendible product bases

Skowronek, Łukasz

doi:10.1063/1.3663836

Cited by 39 publications

(72 citation statements)

References 41 publications

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“…With the aid of theorem 4, one sees that five-qubit PPT symmetric states of ranks (6,9,12), (6,10,11), and (6, 10, 12) are generically not edge (notice that due to Ineq. 60 for the same ranks PPT states cannot be extremal).…”

Section: Special Casesmentioning

confidence: 99%

“…Then, theorem 3 says that if either r(ρ TA ) ≤ 8 or r(ρ TAB ) ≤ 9, they are generically separable. Similarly to the case of N = 4, this leaves six (out of 120 possible under the assumption that r(ρ) = 6) ranks for which typical PPT symmetric states need not be separable: (6, 9, 10), (6,9,11), (6,9,12), (6,10,10), (6,10,11), and (6,10,12).…”

Section: Special Casesmentioning

confidence: 99%

“…60 for the same ranks PPT states cannot be extremal). Hence, analysis of PPT entanglement in in this case reduces to three configurations of ranks (6, 9, 10), (6,10,10), and (6, 9, 11). Interestingly, only in the second case we found examples of extremal states with the above numerical algorithm (see table I).…”

Section: Special Casesmentioning

confidence: 99%

“…This approach has recently been extensively studied (see Refs. [3][4][5][6][7]). In particular, it allowed to solve the open problem of existence of four-qubit PPT entangled symmetric states [8], and also, although in an indirect way, disprove the Peres conjecture in the multipartite case [9].…”

Section: Introductionmentioning

confidence: 99%

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Entangled symmetric states ofNqubits with all positive partial transpositions

et al. 2012

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From both theoretical and experimental points of view symmetric states constitute an important class of multipartite states. Still, entanglement properties of these states, in particular those with positive partial transposition (PPT), lack a systematic study. Aiming at filling in this gap, we have recently affirmatively answered the open question of existence of four-qubit entangled symmetric states with positive partial transposition and thoroughly characterized entanglement properties of such states [J. Tura et al., Phys. Rev. A 85, 060302(R) (2012)] With the present contribution we continue on characterizing PPT entangled symmetric states. On the one hand, we present all the results of our previous work in a detailed way. On the other hand, we generalize them to systems consisting of arbitrary number of qubits. In particular, we provide criteria for separability of such states formulated in terms of their ranks. Interestingly, for most of the cases, the symmetric states are either separable or typically separable. Then, edge states in these systems are studied, showing in particular that to characterize generic PPT entangled states with four and five qubits, it is enough to study only those that assume few (respectively, two and three) specific configurations of ranks. Finally, we numerically search for extremal PPT entangled states in such systems consisting of up to 23 qubits. One can clearly notice regularity behind the ranks of such extremal states, and, in particular, for systems composed of odd number of qubits we find a single configuration of ranks for which there are extremal states.

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Section: Special Casesmentioning

confidence: 99%

Section: Special Casesmentioning

confidence: 99%

Section: Special Casesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Entangled symmetric states ofNqubits with all positive partial transpositions

et al. 2012

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“…The acronym PPTES is also used for an entangled PPT state in the literature with interesting applications to Quantum Information theory appearing mainly in Physics Journals, to name a few, [9], [10], [18], [23], [26], [35], [37], [45], [46] [47], [54], [59], [73], [82].…”

Section: A Notationmentioning

confidence: 99%

Role Of Partial Transpose And Generalized Choi Maps In Quantum Dynamical Semigroups Involving Separable And Entangled States

Singh

2015

ELA

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Abstract. Power symmetric matrices defined and studied by R. Sinkhorn (1981) and their generalization by R.B. Bapat, S.K. Jain and K. Manjunatha Prasad (1999) have been utilized to give positive block matrices with trace one possessing positive partial transpose, the so-called PPT states. Another method to construct such PPT states is given, it uses the form of a matrix unitarily equivalent to its transpose obtained by S.R. Garcia and J.E. Tener (2012). Evolvement or suppression of separability or entanglement of various levels for a quantum dynamical semigroup of completely positive maps has been studied using Choi-Jamiolkowsky matrix of such maps and the famous Horodecki's criteria (1996). A Trichotomy Theorem has been proved, and examples have been given that depend mainly on generalized Choi maps and clearly distinguish the levels of entanglement breaking.

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Guess Your Neighbour’s Input: No Quantum Advantage but an Advantage for Quantum Theory

Acín

Almeida

Augusiak

et al. 2015

Fundamental Theories of Physics

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Quantum mechanics dramatically differs from classical physics, allowing for a wide range of genuinely quantum phenomena. The goal of quantum information is to understand information processing from a quantum perspective. In this mindset, it is thus natural to focus on tasks where quantum resources provide an advantage over classical ones, and to overlook tasks where quantum mechanics provides no advantage. But are the latter tasks really useless from a more general perspective? Here we discuss a simple information-theoretic game called 'guess your neighbour's input', for which classical and quantum players perform equally well. We will see that this seemingly innocuous game turns out to be useful in various contexts. From a fundamental point of view, the game provides a sharp separation between quantum mechanics and other more general physical theories, hence bringing a deeper understanding of the foundations of quantum mechanics. The game also finds unexpected applications in quantum foundations and quantum information theory, related to Gleason's theorem, and to bound entanglement and unextendible product bases.

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Three-by-three bound entanglement with general unextendible product bases

Cited by 39 publications

References 41 publications

Entangled symmetric states ofNqubits with all positive partial transpositions

Entangled symmetric states ofNqubits with all positive partial transpositions

Role Of Partial Transpose And Generalized Choi Maps In Quantum Dynamical Semigroups Involving Separable And Entangled States

Guess Your Neighbour’s Input: No Quantum Advantage but an Advantage for Quantum Theory

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