© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Physical Review A

Typical features of the Mintert-Buchleitner lower bound for concurrence

Antoni Borràs, A. P. Majtey, Angel Ricardo Plastino, M. Casas, Angel Ricardo Plastino

Published Feb 13, 2009• 12 citations

Abstract

Despite the great importance of quantum entanglement, a computationally practical, physically motivated, and experimentally implementable way to estimate the amount of entanglement associated with a general (mixed) state of a bipartite quantum system is still lacking. An entanglement lower bound recently advanced by Mintert and Buchleitner [Phys. Rev. Lett. 98, 140505 (2007)] was proposed as a possible tool for the aforementioned task. Mintert and Buchleitner presented evidence indicating that, due to its tightness, in some important cases the alluded bound can be used as an entanglement measure. From the physical point of view, what makes this bound particularly appealing as an entanglement measure is that it is based on an observable quantity. For this last reason, and also because of its other attractive feature, mathematical simplicity, this promising bound and its possible use as an entanglement estimator certainly deserve to be the focus of careful attention. The usefulness of the bound as an entanglement measure, however, depends on its degree of tightness. Here we perform a systematic survey of the behavior of the alluded bound in state space, in order to determine its typical properties (in particular its tightness) and thus assess its value as an entanglement estimator.

DOI: 10.1103/physreva.79.022112

Related papers

Experimental Examination of Entanglement Estimates

Songbo Xie, Yuanyuan Zhao, Chao Zhang +4 more

Recently, a proper genuine multipartite entanglement measure has been found for three-qubit pure states [see Xie and Eberly, Phys. Rev. Lett. 127, 040403 (2021)PRLTAO0031-900710.1103/PhysRevLett.127.040403], but capturing useful entanglement measures for mixed states has remained an open challenge. So far, it requires not only a full tomography in experiments, but also huge calculational labor. A leading proposal was made by Gühne, Reimpell, and Werner [Phys. Rev. Lett. 98, 110502 (2007)PRLTAO0031-900710.1103/PhysRevLett.98.110502], who used expectation values of entanglement witnesses to describe a lower bound estimation of entanglement. We provide here an extension that also gives genuine upper bounds of entanglement. This advance requires only the expectation value of any Hermitian operator. Moreover, we identify a class of operators A_{1} that not only give good estimates, but also require a remarkably small number of experimental measurements. In this Letter, we define our approach and illustrate it by estimating entanglement measures for a number of pure and mixed states prepared in our recent experiments.

arXiv:2207.07584•Physical Review Letters•Apr 12, 2023•5 citations

Measurable lower bounds on concurrence

Iman Sargolzahi, Sayyed Yahya Mirafzali, Mohsen Sarbishaei

We derive measurable lower bounds on concurrence of arbitrary mixed states, for both bipartite and multipartite cases. First, we construct measurable lower bonds on the \textit{purely algebraic} bounds of concurrence [F. Mintert \textit{et al.} (2004), Phys. Rev. lett., 92, 167902]. Then, using the fact that the sum of the square of the algebraic bounds is a lower bound of the squared concurrence, we sum over our measurable bounds to achieve a measurable lower bound on concurrence. With two typical examples, we show that our method can detect more entangled states and also can give sharper lower bonds than the similar ones.

Quantum Information and Computation•Jan 1, 2011•1 citation

Measurable lower bounds on concurrence

Iman Sargolzahi, Sayyed Yahya Mirafzali, Mohsen Sarbishaei

We derive measurable lower bounds on concurrence of arbitrary mixed states, for both bipartite and multipartite cases. First, we construct measurable lower bonds on the purely algebraic bounds of concurrence [F. Mintert et al. (2004), Phys. Rev. lett., 92, 167902]. Then, using the fact that the sum of the square of the algebraic bounds is a lower bound of the squared concurrence, we sum over our measurable bounds to achieve a measurable lower bound on concurrence. With two typical examples, we show that our method can detect more entangled states and also can give sharper lower bonds than the similar ones.

arXiv:0910.1928•Oct 10, 2009•0 citations

Proof of a lower bound for bipartite concurrence via equivalence to an observable entanglement measure

Xi-Jun Ren, Zheng-Wei Zhou, Xingxiang Zhou +1 more

In this Brief Report, we prove that an analytically solvable two-qubit entanglement monotone introduced by Zhang et al. [Phys. Rev. A 76, 032306 (2007)] is no greater than the square of concurrence. This proof is based on the equivalence between Zhang et al.'s monotone and an observable entanglement measure for mixed states suggested by Mintert and Buchleitner [Phys. Rev. Lett. 98, 140505 (2007)]. Our result may clarify the connections between several recently defined entanglement measures and help understand their possible applications in quantum-information theory.

Physical Review A•May 22, 2008•5 citations

Measurable entanglement

Alexander A. Klyachko, Barış Öztop, A.S. Shumovsky

The amount of entanglement carried by a quantum bipartite state is usually evaluated in terms of concurrence [S. Hill and W. K. Wootters, Phys. Rev. Lett. 78, 5022 (1997); P. Rungta, V. Bužek, C. M. Caves, M. Hillery, and G. J. Milburn, Phys. Rev. A 64, 042315 (2001)]. We give a physical interpretation of concurrence that reveals a way of its direct measurement and discuss possible generalizations.

arXiv:quant-ph/0512197•Applied Physics Letters•Mar 20, 2006•28 citations

Practical method to obtain a lower bound to the three-tangle

Christopher Eltschka, Jens Siewert

The quantitative assessment of the entanglement in multipartite quantum states is, apart from its fundamental importance, a practical problem. Recently there has been significant progress in developing new methods to determine certain entanglement measures. In particular, there is a method---in principle, analytical---to compute a certified lower bound for the three-tangle. The purpose of this work is to provide a manual for the implementation of this approach and to explicitly discuss several analytically solvable cases in order to gauge the numerical tools. Moreover, we derive a simple analytical bound for the mixed-state three-tangle.

arXiv:1310.8311•Physical Review A•Feb 12, 2014•20 citations

Despite the great importance of quantum entanglement, a computationally practical, physically motivated, and experimentally implementable way to estimate the amount of entanglement associated with a general (mixed) state of a bipartite quantum system is still lacking. An entanglement lower bound recently advanced by Mintert and Buchleitner [Phys. Rev. Lett. 98, 140505 (2007)] was proposed as a possible tool for the aforementioned task. Mintert and Buchleitner presented evidence indicating that, due to its tightness, in some important cases the alluded bound can be used as an entanglement measure. From the physical point of view, what makes this bound particularly appealing as an entanglement measure is that it is based on an observable quantity. For this last reason, and also because of its other attractive feature, mathematical simplicity, this promising bound and its possible use as an entanglement estimator certainly deserve to be the focus of careful attention. The usefulness of the bound as an entanglement measure, however, depends on its degree of tightness. Here we perform a systematic survey of the behavior of the alluded bound in state space, in order to determine its typical properties (in particular its tightness) and thus assess its value as an entanglement estimator.

Recently, a proper genuine multipartite entanglement measure has been found for three-qubit pure states [see Xie and Eberly, Phys. Rev. Lett. 127, 040403 (2021)PRLTAO0031-900710.1103/PhysRevLett.127.040403], but capturing useful entanglement measures for mixed states has remained an open challenge. So far, it requires not only a full tomography in experiments, but also huge calculational labor. A leading proposal was made by Gühne, Reimpell, and Werner [Phys. Rev. Lett. 98, 110502 (2007)PRLTAO0031-900710.1103/PhysRevLett.98.110502], who used expectation values of entanglement witnesses to describe a lower bound estimation of entanglement. We provide here an extension that also gives genuine upper bounds of entanglement. This advance requires only the expectation value of any Hermitian operator. Moreover, we identify a class of operators A_{1} that not only give good estimates, but also require a remarkably small number of experimental measurements. In this Letter, we define our approach and illustrate it by estimating entanglement measures for a number of pure and mixed states prepared in our recent experiments.

We derive measurable lower bounds on concurrence of arbitrary mixed states, for both bipartite and multipartite cases. First, we construct measurable lower bonds on the \textit{purely algebraic} bounds of concurrence [F. Mintert \textit{et al.} (2004), Phys. Rev. lett., 92, 167902]. Then, using the fact that the sum of the square of the algebraic bounds is a lower bound of the squared concurrence, we sum over our measurable bounds to achieve a measurable lower bound on concurrence. With two typical examples, we show that our method can detect more entangled states and also can give sharper lower bonds than the similar ones.

We derive measurable lower bounds on concurrence of arbitrary mixed states, for both bipartite and multipartite cases. First, we construct measurable lower bonds on the purely algebraic bounds of concurrence [F. Mintert et al. (2004), Phys. Rev. lett., 92, 167902]. Then, using the fact that the sum of the square of the algebraic bounds is a lower bound of the squared concurrence, we sum over our measurable bounds to achieve a measurable lower bound on concurrence. With two typical examples, we show that our method can detect more entangled states and also can give sharper lower bonds than the similar ones.

In this Brief Report, we prove that an analytically solvable two-qubit entanglement monotone introduced by Zhang et al. [Phys. Rev. A 76, 032306 (2007)] is no greater than the square of concurrence. This proof is based on the equivalence between Zhang et al.'s monotone and an observable entanglement measure for mixed states suggested by Mintert and Buchleitner [Phys. Rev. Lett. 98, 140505 (2007)]. Our result may clarify the connections between several recently defined entanglement measures and help understand their possible applications in quantum-information theory.

The quantitative assessment of the entanglement in multipartite quantum states is, apart from its fundamental importance, a practical problem. Recently there has been significant progress in developing new methods to determine certain entanglement measures. In particular, there is a method---in principle, analytical---to compute a certified lower bound for the three-tangle. The purpose of this work is to provide a manual for the implementation of this approach and to explicitly discuss several analytically solvable cases in order to gauge the numerical tools. Moreover, we derive a simple analytical bound for the mixed-state three-tangle.