Four-qubit entangled symmetric states with positive partial transpositions

Tura, Jordi; Augusiak, Remigiusz; Hyllus, Philipp; Kuś, Marek; Samsonowicz, Jan; Lewenstein, Maciej

doi:10.1103/physreva.85.060302

Cited by 53 publications

(70 citation statements)

References 54 publications

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“…From theorems 2 and 3 it follows that PPT states of ranks (5, r(ρ TA ), r(ρ TAB )) with r(ρ TA ) ≤ 6 or r(ρ TAB ) ≤ 6 are either all separable or generically separable. Then, theorem 6 states that generic PPT states of ranks (5,8,7) are not edge and thus not extremal. Finally, Ineq.…”

Section: B Extremal Ppt Entangled Symmetric Statesmentioning

confidence: 99%

“…Therefore, Eq. (27) We already know that for there exist PPT entangled symmetric states consisting of more than three qubits [8,17,18] and thus indecomposable entanglement witnesses detecting them. Consequently, the above method does not apply in general for even N ≥ 8.…”

Section: Lemma 3 Consider An Equationmentioning

confidence: 99%

“…Recently, the remaining case of N = 4 has been studied in Ref. [8], where the open question as to whether partial transposition serves in this case as a necessary and sufficient condition for separability (as this is the case for N = 2, 3) has been given a negative answer. The main aim of the present paper is to continue the characterization of PPT entanglement in symmetric states.…”

Section: Introductionmentioning

confidence: 99%

“…[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%

“…We discuss in detail methods used in Ref. [8] and then generalize them to the case of arbitrary N . We derive separability criteria for PPT symmetric states in terms of their ranks and ranks of their partial transpositions.…”

Section: Introductionmentioning

confidence: 99%

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Entangled symmetric states ofNqubits with all positive partial transpositions

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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: B Extremal Ppt Entangled Symmetric Statesmentioning

confidence: 99%

Section: Lemma 3 Consider An Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Entangled symmetric states ofNqubits with all positive partial transpositions

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Multidisciplinary Efforts Advance Materials Research at Beihang University

Cheng

Jiang

2017

Advanced Materials

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Gaze estimation methods estimate gaze from facial appearance with a single camera. However, due to the limited view of a single camera, the captured facial appearance cannot provide complete facial information and thus complicate the gaze estimation problem. Recently, camera devices are rapidly updated. Dual cameras are affordable for users and have been integrated in many devices. This development suggests that we can further improve gaze estimation performance with dual-view gaze estimation. In this paper, we propose a dual-view gaze estimation network (DV-Gaze). DV-Gaze estimates dual-view gaze directions from a pair of images. We first propose a dual-view interactive convolution (DIC) block in DV-Gaze. DIC blocks exchange dual-view information during convolution in multiple feature scales. It fuses dual-view features along epipolar lines and compensates for the original feature with the fused feature. We further propose a dual-view transformer to estimate gaze from dual-view features. Camera poses are encoded to indicate the position information in the transformer. We also consider the geometric relation between dual-view gaze directions and propose a dual-view gaze consistency loss for DV-Gaze. DV-Gaze achieves state-of-the-art performance on ETH-XGaze and EVE datasets. Our experiments also prove the potential of dual-view gaze estimation. We release codes in https://github.com/yihuacheng/DVGaze.

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Characterizing Entanglement and Quantum Correlations Constrained by Symmetry

Brugués¹

2017

Springer Theses

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EnglishEntanglement and nonlocal correlations constitute two fundamental resources for quantum information processing, as they allow for novel tasks that are otherwise impossible in a classical scenario. However, their elusive characterization is still a central problem in Quantum Information Theory. The main reason why such a fundamental issue remains a formidable challenge lies in the exponential growth in complexity of the Hilbert space, as well as the space of nonlocal correlations. Physical systems of interest, on the other hand, display symmetries that can be exploited to reduce this complexity, opening the possibility that, for such systems, some of these questions become tractable.This PhD Thesis is dedicated to the study and characterization of entanglement and nonlocal correlations constrained under symmetries. It contains original results in these four threads of research: PPT entanglement in the symmetric states, nonlocality detection in many-body systems, the non-equivalence between entanglement and nonlocality and elemental monogamies of correlations.First, we study PPT entanglement in fully symmetric n-qubit states. We solve the open question on the existence of four-qubit PPT entangled states of these kind, providing constructive examples and methods. Furthermore, we develop criteria for separability, edgeness and the Schmidt number of PPT entangled symmetric states. Geometrically, we focus on the characterization of extremal states of this family and we provide an algorithm to find states with such properties.Second, we study nonlocality in many-body systems. We consider permutationally and translationally invariant Bell inequalities consisting of two-body correlators. These constitute the first tools to detect nonlocality in many-body systems in an experimentally-friendly way with our current technology. Furthermore, we show how these Bell inequalities detect nonloi cality in physically relevant systems such as ground states of Hamiltonians that naturally arise e.g., in nuclear physics. We provide analytical classes of Bell inequalities and we analytically characterize which states and measurements are best suited for them. We show that the method we introduce can be fully generalized to correlators of any order in any Bell scenario. Finally, we provide some feedback from a more experimental point of view.Third, we demonstrate that entanglement and nonlocality are inequivalent concepts in general; a question that remained open in the multipartite case. We show that the strongest form of entanglement, genuinely multipartite entanglement, does not imply the strongest form of nonlocality, genuinely multipartite nonlocality, in any case. We give a constructive method that, starting from a multipartite genuinely multipartite state admitting a K-local model, extends it to a genuinely multipartite entangled state of any number of parties while preserving the degree of locality.Finally, we show that nonlocal correlations are monogamous in a much stronger sense than the typical one, in which th...

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Four-qubit entangled symmetric states with positive partial transpositions

Cited by 53 publications

References 54 publications

Entangled symmetric states ofNqubits with all positive partial transpositions

Entangled symmetric states ofNqubits with all positive partial transpositions

Multidisciplinary Efforts Advance Materials Research at Beihang University

Characterizing Entanglement and Quantum Correlations Constrained by Symmetry

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