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:quant-ph/0504026 · Physical Review A

Noiseless method for checking the Peres separability criterion by local operations and classical communication

Yan-Kui Bai, Shu‐Shen Li, Houzhi Zheng

Published Nov 18, 2005• 7 citations
arXivHTMLPDF

Abstract

We present a method for checking the Peres separability criterion in an arbitrary bipartite quantum state ${\ensuremath{\rho}}_{\mathrm{AB}}$ within local operations and classical communication scenario. The method does not require noise operation which is needed in making the partial transposition map physically implementable. The main task for the two observers, Alice and Bob, is to measure some specific functions of the partial transposed matrix. With these functions, they can determine the eigenvalues of ${\ensuremath{\rho}}_{\mathrm{AB}}^{{T}_{\mathrm{B}}}$, among which the minimum serves as an entanglement witness.

DOI
10.1103/physreva.72.052320

Related papers

Detecting a set of entanglement measures in an unknown tripartite quantum state by local operations and classical communication

Yan-Kui Bai, Shu‐Shen Li, Houzhi Zheng +1 more

We propose a more general method for detecting a set of entanglement measures, i.e., negativities, in an arbitrary tripartite quantum state by local operations and classical communication. To accomplish the detection task using this method, three observers do not need to perform partial transposition maps by the structural physical approximation; instead, they only need to collectively measure some functions via three local networks supplemented by a classical communication. With these functions, they are able to determine the set of negativities related to the tripartite quantum state.

arXiv:quant-ph/0604209•Physical Review A•Aug 4, 2006•1 citation

Noiseless Quantum Circuits for the Peres Separability Criterion

Hilary A. Carteret

In this Letter we give a method for constructing sets of simple circuits that can determine the spectrum of a partially transposed density matrix, without requiring either a tomographically complete positive-operator-valued measurement or the addition of noise to make the spectrum non-negative. These circuits depend only on the dimension of the Hilbert space and are otherwise independent of the state.

arXiv:quant-ph/0309216•Physical Review Letters•Jan 31, 2005•64 citations

Method for measuring two-qubit entanglement of formation by local operations and classical communication

Yan-Kui Bai, Shu‐Shen Li, Houzhi Zheng

We present a parametrically efficient method for measuring the entanglement of formation E-f in an arbitrarily given unknown two-qubit state rho(AB) by local operations and classical communication. The two observers, Alice and Bob, first perform some local operations on their composite systems separately, by which the desired global quantum states can be prepared. Then they estimate seven functions via two modified local quantum networks supplemented a classical communication. After obtaining these functions, Alice and Bob can determine the concurrence C and the entanglement of formation E-f.

Journal of Physics A Mathematical and General•Sep 21, 2005•10 citations

Method for detecting concurrence without the structural physical approximation by local operations and classical communication

Yan-Kui Bai, Shu‐Shen Li, Houzhi Zheng +1 more

We present a modified method for detecting the concurrence in an arbitrary two-qubit quantum state rho(AB) with local operations and classical communication. In this method, it is not necessary for the two observers to prepare the quantum state rho(AB) by the structural physical approximation. Their main task is to measure four specific functions via two local quantum networks. With these functions they can determine the concurrence and then the entanglement of formation.

Journal of Physics A Mathematical and General•May 3, 2006•3 citations

Optimal Entanglement Certification from Moments of the Partial Transpose

Xiao‐Dong Yu, Satoya Imai, Otfried Gühne

For the certification and benchmarking of medium-size quantum devices, efficient methods to characterize entanglement are needed. In this context, it has been shown that locally randomized measurements on a multiparticle quantum system can be used to obtain valuable information on the so-called moments of the partially transposed quantum state. This allows one to infer some separability properties of a state, but how to use the given information in an optimal and systematic manner has yet to be determined. We propose two general entanglement detection methods based on the moments of the partially transposed density matrix. The first method is based on the Hankel matrices and provides a family of entanglement criteria, of which the lowest order reduces to the known p_{3}-positive-partial-transpose criterion proposed in A. Elben et al. [Phys. Rev. Lett. 125, 200501 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.200501]. The second method is optimal and gives necessary and sufficient conditions for entanglement based on some moments of the partially transposed density matrix.

arXiv:2103.06897•Physical Review Letters•Aug 4, 2021•71 citations

Entanglement in SU(2)-invariant quantum systems: The positive partial transpose criterion and others

John Schliemann

We study entanglement in mixed bipartite quantum states which are invariant under simultaneous SU(2) transformations in both subsystems. Previous results on the behavior of such states under partial transposition are substantially extended. The spectrum of the partial transpose of a given SU(2)-invariant density matrix $\ensuremath{\rho}$ is entirely determined by the diagonal elements of $\ensuremath{\rho}$ in a basis of tensor-product states of both spins with respect to a common quantization axis. We construct a set of operators which act as entanglement witnesses on SU(2)-invariant states. A sufficient criterion for $\ensuremath{\rho}$ having a negative partial transpose is derived in terms of a simple spin correlator. The same condition is a necessary criterion for the partial transpose to have the maximum number of negative eigenvalues. Moreover, we derive a series of sum rules which uniquely determine the eigenvalues of the partial transpose in terms of a system of linear equations. Finally we compare our findings with other entanglement criteria including the reduction criterion, the majorization criterion, and the recently proposed local uncertainty relations.

arXiv:quant-ph/0503123•Physical Review A•Jul 11, 2005•36 citations
We present a method for checking the Peres separability criterion in an arbitrary bipartite quantum state \ensuremathρAB{\ensuremath{\rho}}_{\mathrm{AB}}\ensuremathρAB​ within local operations and classical communication scenario. The method does not require noise operation which is needed in making the partial transposition map physically implementable. The main task for the two observers, Alice and Bob, is to measure some specific functions of the partial transposed matrix. With these functions, they can determine the eigenvalues of \ensuremathρABTB{\ensuremath{\rho}}_{\mathrm{AB}}^{{T}_{\mathrm{B}}}\ensuremathρABTB​​, among which the minimum serves as an entanglement witness.
We propose a more general method for detecting a set of entanglement measures, i.e., negativities, in an arbitrary tripartite quantum state by local operations and classical communication. To accomplish the detection task using this method, three observers do not need to perform partial transposition maps by the structural physical approximation; instead, they only need to collectively measure some functions via three local networks supplemented by a classical communication. With these functions, they are able to determine the set of negativities related to the tripartite quantum state.
We present a parametrically efficient method for measuring the entanglement of formation E-f in an arbitrarily given unknown two-qubit state rho(AB) by local operations and classical communication. The two observers, Alice and Bob, first perform some local operations on their composite systems separately, by which the desired global quantum states can be prepared. Then they estimate seven functions via two modified local quantum networks supplemented a classical communication. After obtaining these functions, Alice and Bob can determine the concurrence C and the entanglement of formation E-f.
For the certification and benchmarking of medium-size quantum devices, efficient methods to characterize entanglement are needed. In this context, it has been shown that locally randomized measurements on a multiparticle quantum system can be used to obtain valuable information on the so-called moments of the partially transposed quantum state. This allows one to infer some separability properties of a state, but how to use the given information in an optimal and systematic manner has yet to be determined. We propose two general entanglement detection methods based on the moments of the partially transposed density matrix. The first method is based on the Hankel matrices and provides a family of entanglement criteria, of which the lowest order reduces to the known p_{3}-positive-partial-transpose criterion proposed in A. Elben et al. [Phys. Rev. Lett. 125, 200501 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.200501]. The second method is optimal and gives necessary and sufficient conditions for entanglement based on some moments of the partially transposed density matrix.
We study entanglement in mixed bipartite quantum states which are invariant under simultaneous SU(2) transformations in both subsystems. Previous results on the behavior of such states under partial transposition are substantially extended. The spectrum of the partial transpose of a given SU(2)-invariant density matrix $\ensuremath{\rho}$ is entirely determined by the diagonal elements of $\ensuremath{\rho}$ in a basis of tensor-product states of both spins with respect to a common quantization axis. We construct a set of operators which act as entanglement witnesses on SU(2)-invariant states. A sufficient criterion for $\ensuremath{\rho}$ having a negative partial transpose is derived in terms of a simple spin correlator. The same condition is a necessary criterion for the partial transpose to have the maximum number of negative eigenvalues. Moreover, we derive a series of sum rules which uniquely determine the eigenvalues of the partial transpose in terms of a system of linear equations. Finally we compare our findings with other entanglement criteria including the reduction criterion, the majorization criterion, and the recently proposed local uncertainty relations.