Entanglement measures and purification procedures

@article{Vedral1998EntanglementMA,
  title={Entanglement measures and purification procedures},
  author={Vlatko Vedral and M. B. Plenio},
  journal={Physical Review A},
  year={1998},
  volume={57},
  pages={1619-1633}
}
We improve previously proposed conditions each measure of entanglement has to satisfy. We present a class of entanglement measures that satisfy these conditions and show that the quantum relative entropy and Bures metric generate two measures of this class. We calculate the measures of entanglement for a number of mixed two spin-1/2 systems using the quantum relative entropy, and provide an efficient numerical method to obtain the measures of entanglement in this case. In addition, we prove a… 
View PDF on arXiv
975 Citations
Highly Influential Citations
40
Background Citations
205
Methods Citations
41
Results Citations
2

Figures from this paper

975 Citations

Citation Type

Citation Type

An Extension of Entanglement Measures for Pure States
To quantify the entanglement is one of the most important topics in quantum entanglement theory. An entanglement measure is built from measures for pure states. Conditions when the entanglement…
The entanglement of purification
We introduce a measure of both quantum as well as classical correlations in a quantum state, the entanglement of purification. We show that the (regularized) entanglement of purification is equal to…
A Reversible Theory of Entanglement and its Relation to the Second Law
We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. In stark contrast to the…
Linking a distance measure of entanglement to its convex roof
TLDR
This work presents a new expression for the geometric measure of entanglement in terms of the maximal fidelity with a separable state, and proves that the number of elements in an optimal decomposition w.r.t.the geometric measure is bounded from above by the Caratheodory bound.
A Theory of Entanglement
TLDR
The basis of a theory of entanglement for quantum states is presented, which begins with a classical theory of entangled discrete measures, then treats quantum mechanics and discusses the statistics of bounded operators on a Hilbert space in terms of context coefficients.
The Resource Theory of Entanglement
TLDR
The first result presents a new approach for improving standard witnessing techniques by using additional information obtained within witnessing experiments and thus, cope with unexpected experimental imperfections, and the second result illustrates the use of entanglement witnessing in construction of measures ofEntanglement that are independent of the specific description of measurement devices similar to a Bell scenario.
Epsilon-measures of entanglement
TLDR
It is shown that many properties of the original measure are inherited by the family, in particular weak monotonicity under transformations applied by means of local operations and classical communication (LOCC) and they may increase on average under stochastic LOCC.
Geometric measure of entanglement compared to measures based on fidelity
TLDR
This work will establish a connection between geometric measure of entanglement proposed in [Phys. Rev. A 68, 042307 (2003)] and measures based on fidelity and find a useful expression for fidelity is derived.
Entanglement Quantification in Atomic Ensembles.
TLDR
This work analytically derives the lower bounds of broad families of entanglement criteria based on variances of arbitrary operators and lower bounding the best separable approximation and the generalized robustness only from measurements of first and second moments of the collective spin operator.
Geometric approach to entanglement quantification with polynomial measures
We show that the quantification of entanglement of any rank-2 state with any polynomial entanglement measure can be recast as a geometric problem on the corresponding Bloch sphere. This approach…
...
...

References

SHOWING 1-10 OF 58 REFERENCES
Entanglement purification via separable superoperators
TLDR
This work uses the fact that every EPP is a separable superoperator to give a new upper bound on the rate of EPPs on Bell- diagonal states, and thus on the capacity of Bell-diagonal channels.
Distinguishability and Accessible Information in Quantum Theory
TLDR
This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states, and gives a way of expressing the problem so that it appears as algebraic as that of the problem of finding quantum distinguishability measures.
Asymptotic Attainment for Quantum Relative Entropy
In this paper I proved that quantum relative entropy D(ρ‖σ) can be asymptotically attained by Kullback Leibler divergences of probabilities given by a certain sequence of measurements. The sequence…
Elements of Information Theory
TLDR
The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Complex Variables and Applications
1 Complex Numbers Sums and Products Basic Algebraic Properties Further Properties Vectors and Moduli Complex Conjugates Exponential Form Products and Powers in Exponential Form Arguments of Products…
Methods of Modern Mathematical Physics, Vol 1: Functional Analysis
TLDR
This book is the first volume of a set of three entitled Analysis of Operators and Operator Algebras.
Phys
  • Rev. Lett. 78, 2275
  • 1997
submitted to Phys
  • Rev. A
  • 1997
Phys
  • Rev. A 54, 3824
  • 1996
Phys
  • Rev Lett. 78, 5022
  • 1997
...
...