Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2210.17204 · Physica Scripta

Detecting entanglement harnessing Lindblad structure

Vaibhav Chimalgi, Bihalan Bhattacharya, Suchetana Goswami, Samyadeb Bhattacharya

Published Sep 28, 2023• 2 citations
arXivHTMLPDF

Abstract

Abstract The problem of entanglement detection is a long standing problem in quantum information theory. One of the primary procedures of detecting entanglement is to find the suitable positive but non-completely positive maps. Here we try to give a generic prescription to construct a positive map that can be useful for such scenarios. We study a class of positive maps arising from Lindblad structures. We show that two famous positive maps viz. transposition, reduction map and Choi map can be obtained as a special case of a class of positive maps having Lindblad structure. Generalizing the transposition map to a one parameter family we have used it to detect genuine multipartite entanglement. Finally being motivated by the negativity of entanglement, we have defined a similar measure for genuine multipartite entanglement.

DOI
10.1088/1402-4896/acfe4d

Related papers

Entanglement and distillation from symmetric positive maps

Albert Rico

Recently, a toolkit of highly symmetric techniques employing matrix inequalities has been developed to detect entanglement in various ways. Here we unifiedly explain in detail these methods, and expand them to a new family of positive maps with further detection capabilities. In the simplest case, we generalize the reduction map to detect more generic states using both multiple copies and local filters. Through the Choi-Jamiołkowski isomorphism, this family of maps leads to a construction of multipartite entanglement witnesses. Discussions and examples are provided regarding the detection of states with local positive partial transposition and the use of multiple copies.

arXiv:2502.18446•Physical Review A•Jan 5, 2026•2 citations

Genuine entanglement detection via projection map in multipartite systems

Bivas Mallick, Sumit Nandi

Abstract We present a formalism to detect genuine multipartite entanglement by considering projection map which is a positive but not completely positive map. Projection map has been motivated by the no-pancake theorem which repudiates the existence of a quantum operation that maps the Bloch sphere onto a disk along its equator. The not-complete positivity feature of projection map is explored to investigate genuine multipartite entanglement in arbitrary N-qubit quantum systems. Our proposed framework can detect some important classes of genuinely entangled states in tripartite and quadripartite scenarios. We provide illustrative example to show the efficacy of our formalism to detect a class of tripartite PPT bound entangled states. Finally, we construct a suitable witness operator based on projection map to certify genuine tripartite entanglement, which is likely to be feasible experimentally.

arXiv:2401.03052•Physica Scripta•Aug 21, 2024•4 citations

Genuine-multipartite entanglement criteria based on positive maps

Fabien Clivaz, Marcus Huber, Ludovico Lami +1 more

Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot distinguish if a state is genuinely multipartite entangled or just entangled across some bipartition. We thus generalise this bipartite concept to the multipartite setting by introducing non-positive maps that are positive on the subset of biseparable states but can map to a non-positive element if applied to a genuine multipartite entangled state. We explicitly construct examples of multipartite non-positive maps, obtained from positive maps via a lifting procedure, that in this fashion can reveal genuine multipartite entanglement in a robust way.

arXiv:1609.08126•Journal of Mathematical Physics•Aug 1, 2017•56 citations

Witnessing Genuine Multipartite Entanglement with Positive Maps

Marcus Huber, Ritabrata Sengupta

We derive a general framework that lifts any set of bipartite to multipartite entanglement witnesses and we show how positive maps can naturally be incorporated into this framework. We show that some previous approaches for multipartite entanglement detection are intimately connected to the witnesses derived from partial transposition and that such criteria can easily be outperformed in higher dimensions by nondecomposable maps. As an exemplary case we present a witness that is capable of detecting genuine multipartite entanglement in bound entangled states.

arXiv:1404.7449•Physical Review Letters•Sep 2, 2014•105 citations

Bound Entanglement Detection in 4 ⊗ 4 Systems via Generalized Choi Maps

Mazhar Ali

We construct a family of positive but not completely positive linear maps acting on $M_4(\mathcal{C})$, obtained as a natural extension of Kye’s indecomposable maps defined for $M_3(\mathcal{C})$. We rigorously prove positivity of these maps on 'X' states and employ them to identify a one-parameter family of bipartite quantum states living in the vicinity of maximally mixed state to be entangled even though states are positive under partial transposition (PPT). This provides an explicit example of a family of quantum states with both bound entangled states and free entangled states in $4 \otimes 4$ systems, a regime that remains less characterized compared to lower-dimensional cases. The proposed maps detect entanglement and reveal new structural features of the PPT entangled region in higher dimensions. Our results extend the applicability of positive-map–based entanglement detection and contribute to the systematic understanding of bound entanglement beyond the $3\otimes 3$ and $2 \otimes 4$ systems. In addition, we show that generalized Choi maps simply can not detect well known PPT entangled states for $2 \otimes 4$ systems.

•Feb 6, 2026•0 citations

Detecting genuine multipartite entanglement using moments of positive maps

Saheli Mukherjee, Bivas Mallick, Sahil Gopalkrishna Naik +2 more

Genuine multipartite entanglement (GME) represents the strongest form of entanglement in multipartite systems, providing significant advantages in various quantum information processing tasks. In this work, we propose an experimentally feasible scheme for detecting GME, based on the truncated moments of positive maps. Our method avoids the need for full state tomography, making it scalable for larger systems. We provide illustrative examples of both pure and mixed states to demonstrate the efficacy of our formalism in detecting inequivalent classes of tripartite genuine entanglement. We further demonstrate the detection of quadripartite genuine entanglement, underscoring the effectiveness of our method in identifying entanglement beyond the tripartite case. Finally, we present a proposal for realizing these moments in real experiments.

arXiv:2506.00162•Physical Review A•Nov 18, 2025•6 citations
Abstract The problem of entanglement detection is a long standing problem in quantum information theory. One of the primary procedures of detecting entanglement is to find the suitable positive but non-completely positive maps. Here we try to give a generic prescription to construct a positive map that can be useful for such scenarios. We study a class of positive maps arising from Lindblad structures. We show that two famous positive maps viz. transposition, reduction map and Choi map can be obtained as a special case of a class of positive maps having Lindblad structure. Generalizing the transposition map to a one parameter family we have used it to detect genuine multipartite entanglement. Finally being motivated by the negativity of entanglement, we have defined a similar measure for genuine multipartite entanglement.
Recently, a toolkit of highly symmetric techniques employing matrix inequalities has been developed to detect entanglement in various ways. Here we unifiedly explain in detail these methods, and expand them to a new family of positive maps with further detection capabilities. In the simplest case, we generalize the reduction map to detect more generic states using both multiple copies and local filters. Through the Choi-Jamiołkowski isomorphism, this family of maps leads to a construction of multipartite entanglement witnesses. Discussions and examples are provided regarding the detection of states with local positive partial transposition and the use of multiple copies.
Abstract We present a formalism to detect genuine multipartite entanglement by considering projection map which is a positive but not completely positive map. Projection map has been motivated by the no-pancake theorem which repudiates the existence of a quantum operation that maps the Bloch sphere onto a disk along its equator. The not-complete positivity feature of projection map is explored to investigate genuine multipartite entanglement in arbitrary N-qubit quantum systems. Our proposed framework can detect some important classes of genuinely entangled states in tripartite and quadripartite scenarios. We provide illustrative example to show the efficacy of our formalism to detect a class of tripartite PPT bound entangled states. Finally, we construct a suitable witness operator based on projection map to certify genuine tripartite entanglement, which is likely to be feasible experimentally.
Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot distinguish if a state is genuinely multipartite entangled or just entangled across some bipartition. We thus generalise this bipartite concept to the multipartite setting by introducing non-positive maps that are positive on the subset of biseparable states but can map to a non-positive element if applied to a genuine multipartite entangled state. We explicitly construct examples of multipartite non-positive maps, obtained from positive maps via a lifting procedure, that in this fashion can reveal genuine multipartite entanglement in a robust way.
We derive a general framework that lifts any set of bipartite to multipartite entanglement witnesses and we show how positive maps can naturally be incorporated into this framework. We show that some previous approaches for multipartite entanglement detection are intimately connected to the witnesses derived from partial transposition and that such criteria can easily be outperformed in higher dimensions by nondecomposable maps. As an exemplary case we present a witness that is capable of detecting genuine multipartite entanglement in bound entangled states.
We construct a family of positive but not completely positive linear maps acting on M4(C)M_4(\mathcal{C})M4​(C), obtained as a natural extension of Kye’s indecomposable maps defined for M3(C)M_3(\mathcal{C})M3​(C). We rigorously prove positivity of these maps on 'X' states and employ them to identify a one-parameter family of bipartite quantum states living in the vicinity of maximally mixed state to be entangled even though states are positive under partial transposition (PPT). This provides an explicit example of a family of quantum states with both bound entangled states and free entangled states in 4⊗44 \otimes 44⊗4 systems, a regime that remains less characterized compared to lower-dimensional cases. The proposed maps detect entanglement and reveal new structural features of the PPT entangled region in higher dimensions. Our results extend the applicability of positive-map–based entanglement detection and contribute to the systematic understanding of bound entanglement beyond the 3⊗33\otimes 33⊗3 and 2⊗42 \otimes 42⊗4 systems. In addition, we show that generalized Choi maps simply can not detect well known PPT entangled states for 2⊗42 \otimes 42⊗4 systems.
Genuine multipartite entanglement (GME) represents the strongest form of entanglement in multipartite systems, providing significant advantages in various quantum information processing tasks. In this work, we propose an experimentally feasible scheme for detecting GME, based on the truncated moments of positive maps. Our method avoids the need for full state tomography, making it scalable for larger systems. We provide illustrative examples of both pure and mixed states to demonstrate the efficacy of our formalism in detecting inequivalent classes of tripartite genuine entanglement. We further demonstrate the detection of quadripartite genuine entanglement, underscoring the effectiveness of our method in identifying entanglement beyond the tripartite case. Finally, we present a proposal for realizing these moments in real experiments.