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

Robustness of Entanglement for Bell Decomposable States

Akhtarshenas, S J, Jafarizadeh, M A

Published Aug 3, 2002• 2 citations
OpenAlex

Abstract

We propose a simple geometrical approach for finding the robustness of entanglement for Bell decomposable states of 2 otimes 2 quantum systems. It is shown that the robustness of entanglement is equal to the concurrence. We also present an analytical expression for two separable states that wipe out all entanglement of these states. Finally the random robustness of these states is also obtained.

Related papers

Robustness of entanglement for two qubit density matrix

Seyed Javad Akhtarshenas, M. A. Jafarizadeh

By considering the decomposition of a generic two qubit density matrix presented by Wootters [W. K. Wootters, Phys. Rev. Lett. {\bf 80} 2245 (1998)], the robustness of entanglement for any mixed state of two qubit systems is obtained algebraically. It is shown that the robustness of entanglement is proportional to concurrence and in Bell decomposable density matrices it is equal to the concurrence. We also give an analytic expression for two separable states which wipe out all entanglement of these states. Since thus obtained robustness is function of the norm of the vectors in the decomposition we give an explicit parameterization for the decomposition.

arXiv:quant-ph/0211156•Nov 24, 2002•1 citation

EXACT CALCULATION OF ROBUSTNESS OF ENTANGLEMENT VIA CONVEX SEMI-DEFINITE PROGRAMMING

M. A. Jafarizadeh, Mehdi Mirzaee, M. Rezaee

In general, the calculation of robustness of entanglement for the mixed entangled quantum states is rather difficult to handle analytically. Using the convex semi-definite programming method, we claculate exactly the robustness of entanglement of some mixed entangled quantum states such as the generic two-qubit state in the Wootters basis, 2 ⊗ 2 Bell decomposable (BD) states, iso-concurrence decomposable states, 2 ⊗ 3 Bell decomposable states, d ⊗ d Werner and isotropic states, a one parameter 3 ⊗ 3 state and a multi-partite isotropic state. The results are in agreement with those of 2 ⊗ 2 density matrices and have already been calculated in Refs. 1 and 2. Also, an analytic expression is given for separable states that wipe out all the entanglements. It is further shown that they are on the boundary of separable states, as pointed out in Ref. 3.

arXiv:quant-ph/0608225•International Journal of Quantum Information•Sep 1, 2005•12 citations

Derivation of the robustness from the concurrence

Yuri Krynytskyi, Andrij Romanovych Kuzmak

Adding the maximally mixed state with some weight to the entanglement system leads to disentanglement of the latter. For each predefined entangled state there exists a minimal value of this weight for which the system loses its entanglement properties. These values were proposed to be used as a quantitative measure of entanglement called robustness [G. Vidal and R. Tarrach, Phys. Rev. A 59, 141 (1999)]. Using the concurrence, we propose the derivation of this measure for the system of two-qubit. Namely, for a two-qubit pure state, an exact expression of robustness is obtained. Finally, in the same way, the robustness of special cases of mixed two-qubit states is calculated.

arXiv:1811.03118•Modern Physics Letters A•Jul 28, 2021•3 citations

Connecting the generalized robustness and the geometric measure of entanglement

Daniel Cavalcanti

The main goal of this paper is to provide a connection between the generalized robustness of entanglement $({R}_{g})$ and the geometric measure of entanglement $({E}_{GME})$. First, we show that the generalized robustness is always higher than or equal to the geometric measure. Then we find a tighter lower bound to ${R}_{g}(\ensuremath{\rho})$ based only on the purity of $\ensuremath{\rho}$ and its maximal overlap to a separable state. As we will see it is also possible to express this lower bound in terms of ${E}_{GME}$.

arXiv:quant-ph/0602031•Physical Review A•Apr 20, 2006•44 citations

Robustness of entanglement

Guifré Vidal, R. Tarrach

In the quest to completely describe entanglement in the general case of a finite number of parties sharing a physical system of finite-dimensional Hilbert space an entanglement magnitude is introduced for its pure and mixed states: robustness. It corresponds to the minimal amount of mixing with locally prepared states which washes out all entanglement. It quantifies in a sense the endurance of entanglement against noise and jamming. Its properties are studied comprehensively. Analytical expressions for the robustness are given for pure states of two-party systems, and analytical bounds for mixed states of two-party systems. Specific results are obtained mainly for the qubit-qubit system (qubit denotes quantum bit). As by-products local pseudomixtures are generalized, a lower bound for the relative volume of separable states is deduced, and arguments for considering convexity a necessary condition of any entanglement measure are put forward.

arXiv:quant-ph/9806094•Physical Review A•Jan 1, 1999•600 citations

Bell scenarios in which nonlocality and entanglement are inversely related

Giuseppe Vallone, G. Lima, Esteban S. Gómez +4 more

We show that for two-qubit chained Bell inequalities with an arbitrary number of measurement settings, nonlocality and entanglement are not only different properties but are inversely related. Specifically, we analytically prove that in absence of noise, robustness of nonlocality, defined as the maximum fraction of detection events that can be lost such that the remaining ones still do not admit a local model, and concurrence are inversely related for any chained Bell inequality with an arbitrary number of settings. The closer quantum states are to product states, the harder it is to reproduce quantum correlations with local models. We also show that, in presence of noise, nonlocality and entanglement are simultaneously maximized only when the noise level is equal to the maximum level tolerated by the inequality; in any other case, a more nonlocal state is always obtained by reducing the entanglement. In addition, we observed that robustness of nonlocality and concurrence are also inversely related for the Bell scenarios defined by the tight two-qubit three-setting ${I}_{3322}$ inequality, and the tight two-qutrit inequality ${I}_{3}$.

arXiv:1106.2240•Physical Review A•Jan 3, 2014•15 citations
We propose a simple geometrical approach for finding the robustness of entanglement for Bell decomposable states of 2 otimes 2 quantum systems. It is shown that the robustness of entanglement is equal to the concurrence. We also present an analytical expression for two separable states that wipe out all entanglement of these states. Finally the random robustness of these states is also obtained.
By considering the decomposition of a generic two qubit density matrix presented by Wootters [W. K. Wootters, Phys. Rev. Lett. {\bf 80} 2245 (1998)], the robustness of entanglement for any mixed state of two qubit systems is obtained algebraically. It is shown that the robustness of entanglement is proportional to concurrence and in Bell decomposable density matrices it is equal to the concurrence. We also give an analytic expression for two separable states which wipe out all entanglement of these states. Since thus obtained robustness is function of the norm of the vectors in the decomposition we give an explicit parameterization for the decomposition.
In general, the calculation of robustness of entanglement for the mixed entangled quantum states is rather difficult to handle analytically. Using the convex semi-definite programming method, we claculate exactly the robustness of entanglement of some mixed entangled quantum states such as the generic two-qubit state in the Wootters basis, 2 ⊗ 2 Bell decomposable (BD) states, iso-concurrence decomposable states, 2 ⊗ 3 Bell decomposable states, d ⊗ d Werner and isotropic states, a one parameter 3 ⊗ 3 state and a multi-partite isotropic state. The results are in agreement with those of 2 ⊗ 2 density matrices and have already been calculated in Refs. 1 and 2. Also, an analytic expression is given for separable states that wipe out all the entanglements. It is further shown that they are on the boundary of separable states, as pointed out in Ref. 3.
Adding the maximally mixed state with some weight to the entanglement system leads to disentanglement of the latter. For each predefined entangled state there exists a minimal value of this weight for which the system loses its entanglement properties. These values were proposed to be used as a quantitative measure of entanglement called robustness [G. Vidal and R. Tarrach, Phys. Rev. A 59, 141 (1999)]. Using the concurrence, we propose the derivation of this measure for the system of two-qubit. Namely, for a two-qubit pure state, an exact expression of robustness is obtained. Finally, in the same way, the robustness of special cases of mixed two-qubit states is calculated.
The main goal of this paper is to provide a connection between the generalized robustness of entanglement (Rg)({R}_{g})(Rg​) and the geometric measure of entanglement (EGME)({E}_{GME})(EGME​). First, we show that the generalized robustness is always higher than or equal to the geometric measure. Then we find a tighter lower bound to ${R}_{g}(\ensuremath{\rho})$ based only on the purity of $\ensuremath{\rho}$ and its maximal overlap to a separable state. As we will see it is also possible to express this lower bound in terms of EGME{E}_{GME}EGME​.
In the quest to completely describe entanglement in the general case of a finite number of parties sharing a physical system of finite-dimensional Hilbert space an entanglement magnitude is introduced for its pure and mixed states: robustness. It corresponds to the minimal amount of mixing with locally prepared states which washes out all entanglement. It quantifies in a sense the endurance of entanglement against noise and jamming. Its properties are studied comprehensively. Analytical expressions for the robustness are given for pure states of two-party systems, and analytical bounds for mixed states of two-party systems. Specific results are obtained mainly for the qubit-qubit system (qubit denotes quantum bit). As by-products local pseudomixtures are generalized, a lower bound for the relative volume of separable states is deduced, and arguments for considering convexity a necessary condition of any entanglement measure are put forward.
We show that for two-qubit chained Bell inequalities with an arbitrary number of measurement settings, nonlocality and entanglement are not only different properties but are inversely related. Specifically, we analytically prove that in absence of noise, robustness of nonlocality, defined as the maximum fraction of detection events that can be lost such that the remaining ones still do not admit a local model, and concurrence are inversely related for any chained Bell inequality with an arbitrary number of settings. The closer quantum states are to product states, the harder it is to reproduce quantum correlations with local models. We also show that, in presence of noise, nonlocality and entanglement are simultaneously maximized only when the noise level is equal to the maximum level tolerated by the inequality; in any other case, a more nonlocal state is always obtained by reducing the entanglement. In addition, we observed that robustness of nonlocality and concurrence are also inversely related for the Bell scenarios defined by the tight two-qubit three-setting I3322{I}_{3322}I3322​ inequality, and the tight two-qutrit inequality I3{I}_{3}I3​.