A comparative study of relative entropy of entanglement, concurrence and negativity

  title={A comparative study of relative entropy of entanglement, concurrence and negativity},
  author={Adam Miranowicz and Andrzej Grudka},
  journal={Journal of Optics B-quantum and Semiclassical Optics},
The problem of ordering of two-qubit states imposed by the relative entropy of entanglement (E )i n comparison with the concurrence (C )a ndnegativity (N )i s studied. Analytical examples of states consistently and inconsistently ordered by the entanglemen tm easures are given. In particular, the states for which any of the three measures imposes order opposite to that given by the other two measures are described. Moreover, examples are given of pairs of 

Figures and Tables from this paper

An analysis of concurrence entanglement measure and quantum fisher information of quantum communication networks of two-qubits
This work studies the state ordering of the two-qubit systems with respect to Quantum Fisher Information vs. Concurrence, and presents the results which are interesting when compared to that of two-level systems. Expand
Comparison of the relative entropy of entanglement and negativity
It is well known that for two qubits the upper bounds of the relative entropy of entanglement (REE) for a given concurrence as well as the negativity for a given concurrence are reached by pureExpand
Quantifying entanglement resources
We present an overview of the quantitative theory of single-copy entanglement in finite-dimensional quantum systems. In particular we emphasize the point of view that different entanglement measuresExpand
Analysis of Entanglement Measures and LOCC Maximized Quantum Fisher Information of General Two Qubit Systems
This work revisits the state ordering problem of general two qubit states and calculates the maximized quantum Fisher information (QFI), showing that there are pairs of states having equal maximized QFI but different values for concurrence, REE and negativity and vice versa. Expand
Probing the relationship between quantum entanglement and non-locality for different states
The relationship between quantum entanglement and non-locality is studied in a two-qubit system for pure states and Werner states. It is found that Werner states are more entangled than pure statesExpand
Towards an entanglement measure for mixed states in CFTs based on relative entropy
A bstractRelative entropy of entanglement (REE) is an entanglement measure of bipartite mixed states, defined by the minimum of the relative entropy S(ρAB ||σAB ) between a given mixed state ρAB andExpand
An Introduction to Entanglement Theory
We review the theory of entanglement measures, concentrating mostly on the finite dimensional two-party case. We begin with a non technical introduction, followed by topics such as: single-copy andExpand
Quantum Discord of 2n-Dimensional Bell-Diagonal States
In this study, using the concept of relative entropy as a distance measure of correlations we investigate the important issue of evaluating quantum correlations such as entanglement, dissonance andExpand
The relation between majorization theory and quantum information from entanglement monotones perspective
Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known monotones for quantifyingExpand
Detecting identical entanglement pure states for two qubits
Entanglement is one of the most surprising features of composite quantum systems. Yet, challenges remain in our understanding and quantification of the entanglement. There is no unique degree ofExpand


A comparison of the entanglement measures negativity and concurrence
In this paper we investigate two different entanglement measures in the case of mixed states of two qubits. We prove that the negativity of a state can never exceed its concurrence and is alwaysExpand
Ordering two-qubit states with concurrence and negativity
We study the ordering of two-qubit states with respect to the degree of bipartite entanglement using the Wootters concurrence - a measure of the entanglement of formation - and the negativity - aExpand
Continuity of relative entropy of entanglement
Abstract We show that an entanglement measure called relative entropy of entanglement satisfies a strong continuity condition. If two states are close to each other then so are their entanglementsExpand
On the volume of the set of mixed entangled states II
A natural measure in the space of density matrices describing N-dimensional quantum systems is proposed. We study the probability P that a quantum state chosen randomly with respect to the naturalExpand
Relativity of Pure States Entanglement
Abstract Entanglement of any pure state of an N × N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures ofExpand
Binegativity and geometry of entangled states in two qubits
We prove that the binegativity is always positive for any two-qubit state. As a result, and as suggested by previous work, the asymptotic relative entropy of entanglement in two qubits does notExpand
Entanglement of formation and concurrence
  • W. Wootters
  • Computer Science, Mathematics
  • Quantum Inf. Comput.
  • 2001
The current understanding of entanglement of formation and the related concept of concurrence is reviewed, including discussions of additivity, the problem of finding explicit formulas, and connections between concurrence and other properties of bipartite states. Expand
Entanglement of Formation of an Arbitrary State of Two Qubits
The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state is defined as the minimum averageExpand
Limits for entanglement measures.
It is shown that any entanglement measure E suitable for the regime of a high number of identically prepared entangled pairs satisfies ED < or = E = or = EF, where ED and EF are theEntanglement of distillation and formation, respectively. Expand
Entanglement measures under symmetry
We show how to simplify the computation of the entanglement of formation and the relative entropy of entanglement for states, which are invariant under a group of local symmetries. For severalExpand