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

Abstract

The problem of ordering of two-qubit states imposed by relative entropy of entanglement (E) in comparison to concurrence (C) and negativity (N) is studied. Analytical examples of states consistently and inconsistently ordered by the entanglement measures 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 the states, for which (i) N'=N" and C'=C" but E' is different from E", (ii) N'=N" and E'=E" but C' differs from C", (iii) E'=E", N'<N" and C'>C", or (iv) states having the same E, C, and N but still violating the Bell-Clauser-Horne-Shimony-Holt inequality to different degrees.

The relation between majorization theory and quantum information from entanglement monotones perspective

“…Due to their findings, in some pairs; for the first system the first measurement is greater than the one for the second system. In another measurement, the result is vice versa [2,3]. This result explains that quantum entanglement measures reflect different particularities of quantum systems.…”

“…In the bipartite case, there are well known monotones for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. The study on these monotones has been a hot topic in quantum information [1][2][3][4][5][6][7] in order to understand the role of entanglement in this discipline. It can be observed that from any arbitrary quantum pure state a mixed state can obtained.…”

Analysis of Negativity and Relative Entropy of Entanglement Measures for Two Qutrit Quantum Communication Systems

“…For example Shors factorization algorithm, Grovers search algorithm, Quantum Fourier Transformation etc. [1][2][3][4][5][6][7][8][9]. On the other hand, lot of work such as the quantum teleportation, super dense coding and quantum key distrubution (QKD) are not possible with classical mechanical systems, they are only possible with quantum mechanical counterparts.…”

Detecting Violation of Bell Inequalities using LOCC Maximized Quantum Fisher Information and Entanglement Measures

“…REE is based on the distance of the state to the closest separable state. Although the value of such measures for separable states turns to be 0, and 1 for maximally entangled states, it was found that this is not the case for the states in between [6][7][8][9][45][46][47]: There are pairs of states that have equal values of one measure but different values of another measure.…”