International Journal of Modern Physics C

A COMPARATIVE STUDY OF NEGATIVITY AND CONCURRENCE BASED ON SPIN COHERENT STATES

K. Berrada, M. El Baz, Hichem Eleuch, Y. Hassouni

Published Mar 1, 2010• 50 citations

Abstract

In this paper, we investigate two different entanglement measures, the negativity and concurrence, in the case of pure and mixed states of two-qubit system basing on the spin coherent states. For two-qubit pure states, the negativity is the same as the concurrence. For mixed states, using a simplified expression of concurrence in Wootters' measure of entanglement, we write the bounds of Verstraete et al.1as a function of some new parameters and we compare the both measures for a class of mixed states.

DOI: 10.1142/s0129183110015129

Related papers

NEGATIVITY OF TWO-QUBIT SYSTEM THROUGH SPIN COHERENT STATES

K. Berrada, Abdus Salam, M. El Baz +1 more

Using the negativity, we express and analyze the entanglement of two-qubit nonorthogonal pure states through the spin coherent states. We formulate this measure in terms of the amplitudes of coherent states and we give the conditions for the minimal and the maximal entanglement. We generalize this formalism to the case of a class of mixed states and show that the negativity is also a function of probabilities.

Jan 1, 20090 citations

ENTANGLEMENT OF TWO-QUBIT NONORTHOGONAL STATES

K. Berrada, A. Chafik, Hichem Eleuch +1 more

We studied the entangled two-qubit nonorthogonal pure states through spin coherent states. Using the concurrence as a measure of entanglement we express it as a function of the amplitudes of those states and find conditions for maximal and minimal entanglement.

International Journal of Modern Physics BMar 30, 200912 citations

Estimation of entanglement negativity of a two-qubit quantum system with two measurements

Satyabrata Adhikari

Numerous work had been done to quantify the entanglement of a two-qubit quantum state, but it can be seen that previous works were based on joint measurements on two copies or more than two copies of the quantum state under consideration. In this work, we show that a single copy and two measurements are enough to estimate the entanglement quantifier like entanglement negativity and concurrence. To achieve our goal, we establish a relationship between the entanglement negativity and the minimum eigenvalue of the structural physical approximation of the partial transpose of an arbitrary two-qubit state. The derived relation makes it possible to estimate entanglement negativity experimentally by Hong-Ou-Mandel interferometry with only two detectors. Also, we derive the upper bound of the concurrence of an arbitrary two-qubit state and have shown that the upper bound can be realized in experiment. We will further show that the concurrence of i) an arbitrary pure two-qubit state and ii) a particular class of mixed states, namely, rank-2 quasi-distillable mixed states, can be exactly estimated with two measurements.

arXiv:1808.09745Europhysics Letters (EPL)Dec 14, 20183 citations

Ordering two-qubit states with concurrence and negativity

Adam Miranowicz, Andrzej Grudka

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---a measure of the entanglement cost under the positive-partial-transpose-preserving operations. For two-qubit pure states, the negativity is the same as the concurrence. However, we demonstrate analytically on simple examples of various mixtures of Bell and separable states that the entanglement measures can impose different orderings on the states. We show which states, in general, give the maximally different predictions (i) when one of the states has the concurrence greater but the negativity smaller than those for the other state and (ii) when the states are entangled to the same degree according to one of the measures, but differently according to the other.

arXiv:quant-ph/0404053Physical Review ASep 28, 200498 citations

Entanglement of General Two-Qubit States in a Realistic Framework

S. Abdel‐Khalek, K. Berrada, Eied Mahmoud Khalil +1 more

In the present paper, we examine the quantum entanglement for more general states of two-qubit system in the context of spin coherent states (SCSs). We consider the concurrence as a quantifier of entanglement and express it in terms of SCSs. We determine new set of maximally entangled conditions that provide the maximal amount of entanglement for certain values of the amplitudes of SCSs for the case of pure states. Finally, we examine the entanglement of a class of mixed states of the two qubits and provide the range in which the entanglement value is maximal with respect to the values of the amplitudes of SCSs.

SymmetryFeb 27, 20212 citations

Comparative analysis of entanglement measures based on monogamy inequality

P. J. Geetha, Sudha, K. S. Mallesh

We evaluate the monogamy inequality for symmetric, non-symmetric pure states of importance in terms of squared concurrence, squared entanglement of formation, squared negativity of partial transpose and compare the corresponding tangles. We show that though concurrence and concurrence tangle are zero for two special classes of mixed entangled states, both negativity tangle and entanglement of formation (EOF) tangle turn out to be non-zero. A comparison of different tangles is carried out in each case and it is shown that while the concurrence tangle captures the genuine multiqubit entanglement in N -qubit pure states with N distinct spinors (containing GHZ and superposition of W-, obverse W states) either negativity tangle or EOF tangle is to be used as a better measure of entanglement in the W-class of states with two distinct spinors and in the special classes of mixed multiqubit states.

Chinese Physics BMay 1, 20174 citations