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

Quantifying the activation power of bipartite entangled states

Fgsl Brandão

Published Oct 12, 2005• 2 citations
OpenAlex

Abstract

We show that the maximum percentual increase that a given bipartite entangled state may provide in the fidelity of teleportation of another arbitrary state is equal to the its generalized robustness of entanglement. In this way, we find a fully operational measure of entanglement in the single-copy level which is strictly positive on all entangled (free and bound) states. Moreover, we highlight the role of entanglement witnesses in this approach.

Related papers

Entanglement activation and the robustness of quantum correlations

Fernando G. S. L. Brandão

We show that the usefulness of a state as an activator in teleportation protocols is equivalent to the robustness of its entanglement to noise. The robustness of entanglement of a bipartite state $\ensuremath{\sigma}$ is linked to the maximum increase in the fidelity of teleportation of any other state when $\ensuremath{\sigma}$ is used as an extra resource. On the one hand, this connection gives an operational meaning to the robustness of entanglement. On the other hand, it shows that the activation capability---which has a central role as an operational way of quantifying bound entangled states---can be estimated experimentally by measuring entanglement witnesses.

arXiv:quant-ph/0510078•Physical Review A•Sep 5, 2007•19 citations

Quantifying entanglement with witness operators

Fernando G. S. L. Brandão

We present a unifying approach to the quantification of entanglement based on entanglement witnesses, which includes several already established entanglement measures such as the negativity, the concurrence, and the robustness of entanglement. We then introduce an infinite family of new entanglement quantifiers, having as its limits the best separable approximation measure and the generalized robustness. Gaussian states, states with symmetry, states constrained to super-selection rules, and states composed of indistinguishable particles are studied under the view of the witnessed entanglement. We derive new bounds to the fidelity of teleportation ${d}_{\mathit{min}}$, for the distillable entanglement ${E}_{D}$ and for the entanglement of formation. A particular measure, the PPT-generalized robustness, stands out due to its easy calculability and provides sharper bounds to ${d}_{\mathit{min}}$ and ${E}_{D}$ than the negativity in most of the states. We illustrate our approach studying thermodynamical properties of entanglement in the Heisenberg XXX and dimerized models.

arXiv:quant-ph/0503152•Physical Review A•Aug 12, 2005•241 citations

Computable measure of entanglement

Guifré Vidal, Reinhard F. Werner

We present a measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system. We show that it does not increase under local manipulations of the system, and use it to obtain a bound on the teleportation capacity and on the distillable entanglement of mixed states.

arXiv:quant-ph/0102117•Physical Review A•Feb 22, 2002•4,901 citations

Certification of Genuine Multipartite Entanglement with General and Robust Device-Independent Witnesses

Chao Zhang, Wen-Hao Zhang, Pavel Sekatski +12 more

Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device independently. However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty in identifying optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this Letter, we explore a general and robust device-independent method that can be applied to various realistic multipartite quantum states in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly entangled Greenberger-Horne-Zeilinger states, showing that the method applies equally well to less standard states.

arXiv:2108.12764•Physical Review Letters•Oct 31, 2022•10 citations

Bounding the Amount of Entanglement from Witness Operators

Liang-Liang Sun, Xiang Zhou, Armin Tavakoli +2 more

We present an approach to estimate the operational distinguishability between an entangled state and any separable state directly from measuring an entanglement witness. We show that this estimation also implies bounds on a variety of other well-known entanglement quantifiers. This approach for entanglement estimation is then extended to both the measurement-device-independent scenario and the fully device-independent scenario, where we obtain nontrivial but suboptimal bounds. The procedure requires no numerical optimization and is easy to compute. It offers ways for experimenters to not only detect, but also quantify, entanglement from the standard entanglement witness procedure.

arXiv:2312.04897•Physical Review Letters•Mar 12, 2024•16 citations

Maximal entanglement — A new measure of entanglement

Salman Beigi

Maximal correlation is a measure of correlation for bipartite distributions. This measure has two intriguing features: (1) it is monotone under local stochastic maps; (2) it gives the same number when computed on i.i.d. copies of a pair of random variables. This measure of correlation has recently been generalized for bipartite quantum states, for which the same properties have been proved. In this paper, based on maximal correlation, we define a new measure of entanglement which we call maximal entanglement. We show that this measure of entanglement is faithful (is zero on separable states and positive on entangled states), is monotone under local quantum operations, and gives the same number when computed on tensor powers of a bipartite state.

arXiv:1405.2502•Iran Workshop on Communication and Information Theory (IWCIT)•May 1, 2014•1 citation
We show that the maximum percentual increase that a given bipartite entangled state may provide in the fidelity of teleportation of another arbitrary state is equal to the its generalized robustness of entanglement. In this way, we find a fully operational measure of entanglement in the single-copy level which is strictly positive on all entangled (free and bound) states. Moreover, we highlight the role of entanglement witnesses in this approach.
We show that the usefulness of a state as an activator in teleportation protocols is equivalent to the robustness of its entanglement to noise. The robustness of entanglement of a bipartite state $\ensuremath{\sigma}$ is linked to the maximum increase in the fidelity of teleportation of any other state when $\ensuremath{\sigma}$ is used as an extra resource. On the one hand, this connection gives an operational meaning to the robustness of entanglement. On the other hand, it shows that the activation capability---which has a central role as an operational way of quantifying bound entangled states---can be estimated experimentally by measuring entanglement witnesses.
We present a unifying approach to the quantification of entanglement based on entanglement witnesses, which includes several already established entanglement measures such as the negativity, the concurrence, and the robustness of entanglement. We then introduce an infinite family of new entanglement quantifiers, having as its limits the best separable approximation measure and the generalized robustness. Gaussian states, states with symmetry, states constrained to super-selection rules, and states composed of indistinguishable particles are studied under the view of the witnessed entanglement. We derive new bounds to the fidelity of teleportation dmin{d}_{\mathit{min}}dmin​, for the distillable entanglement ED{E}_{D}ED​ and for the entanglement of formation. A particular measure, the PPT-generalized robustness, stands out due to its easy calculability and provides sharper bounds to dmin{d}_{\mathit{min}}dmin​ and ED{E}_{D}ED​ than the negativity in most of the states. We illustrate our approach studying thermodynamical properties of entanglement in the Heisenberg XXX and dimerized models.
Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device independently. However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty in identifying optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this Letter, we explore a general and robust device-independent method that can be applied to various realistic multipartite quantum states in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly entangled Greenberger-Horne-Zeilinger states, showing that the method applies equally well to less standard states.
We present an approach to estimate the operational distinguishability between an entangled state and any separable state directly from measuring an entanglement witness. We show that this estimation also implies bounds on a variety of other well-known entanglement quantifiers. This approach for entanglement estimation is then extended to both the measurement-device-independent scenario and the fully device-independent scenario, where we obtain nontrivial but suboptimal bounds. The procedure requires no numerical optimization and is easy to compute. It offers ways for experimenters to not only detect, but also quantify, entanglement from the standard entanglement witness procedure.
Maximal correlation is a measure of correlation for bipartite distributions. This measure has two intriguing features: (1) it is monotone under local stochastic maps; (2) it gives the same number when computed on i.i.d. copies of a pair of random variables. This measure of correlation has recently been generalized for bipartite quantum states, for which the same properties have been proved. In this paper, based on maximal correlation, we define a new measure of entanglement which we call maximal entanglement. We show that this measure of entanglement is faithful (is zero on separable states and positive on entangled states), is monotone under local quantum operations, and gives the same number when computed on tensor powers of a bipartite state.