Bipartite entanglement measure based on covariances (original) (raw)
Related papers
Bipartite entanglement measure based on covariance
Physical Review A, 2007
We propose an entanglement measure for two quN its based on the covariances of a set of generators of the su(N ) algebra. In particular, we represent this measure in terms of the mutually unbiased projectors for N prime. For pure states this measure quantify entanglement, we obtain an explicit expression which relates it to the concurrence hierarchy, specifically the I-concurrence and the 3concurrence. For mixed states we propose a separability criterion.
Information-Theoretic Measure of Genuine Multi-Qubit Entanglement
2006
We consider pure quantum states of N qubits and study the genuine N −qubit entanglement that is shared among all the N qubits. We introduce an information-theoretic measure of genuine N -qubit entanglement based on bipartite partitions. When N is an even number, this measure is presented in a simple formula, which depends only on the purities of the partially reduced density matrices. It can be easily computed theoretically and measured experimentally. When N is an odd number, the measure can also be obtained in principle. 03.65.Ud, 73.43.Nq, 89.70.+c The nature of quantum entanglement is a fascinating topic in quantum mechanics since the famous Einstein-Podolsky-Rosen paper [1] in 1935. Recently, much interest has been focused on entanglement in quantum systems containing a large number of particles. On one hand, multipartite entanglement is valuable physical resource in large-scale quantum information processing . On the other hand, multipartite entanglement seems to play an important role in condensed matter physics [4], such as quantum phase transitions (QPT) and high temperature superconductivity . Therefore, how to characterize and quantify multipartite entanglement remains one of the central issues in quantum information theory.
Entanglement and Its Multipartite Extensions
International Journal of Modern Physics B, 2013
The aspects of many particle systems as far as their entanglement is concerned is highlighted. To this end we briefly review the bipartite measures of entanglement and the entanglement of pairs both for systems of distinguishable and indistinguishable particles. The analysis of these quantities in macroscopic systems shows that close to quantum phase transitions, the entanglement of many particles typically dominates that of pairs. This leads to an analysis of a method to construct many-body entanglement measures. SL-invariant measures are a generalization to quantities as the concurrence, and can be obtained with a formalism containing two (actually three) orthogonal antilinear operators. The main drawback of this antilinear framework, namely to measure these quantities in the experiment, is resolved by a formula linking the antilinear formalism to an equivalent linear framework.
Evaluable multipartite entanglement measures: Multipartite concurrences as entanglement monotones
Physical Review A, 2006
We discuss the monotonicity of systematically constructed quantities aiming at the quantification of the entanglement properties of multipartite quantum systems, under local operations and classical communication (LOCC). We provide a necessary and sufficient condition for the monotonicity of generalized multipartite concurrences which qualifies them as legitimate entanglement measures.
Entanglement Monotones and Maximally Entangled States in Multipartite Qubit Systems
International Journal of Quantum Information, 2006
We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call comb in reference to the hairy-ball theorem. For qubits (or spin 1/2) the combs are automatically invariant under SL(2, C). This implies that the filters obtained from the combs are entanglement monotones by construction. We give alternative formulae for the concurrence and the 3-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-, five-and six-qubit entanglement.
ENTANGLEMENT MEASURE FOR A MULTIPARTITE PURE STATE
dti.unimi.it
This work concerns with the problem of quantifing entanglement in pure states of multipartite two-levels systems. We adopt an information theoretical approach using information entropy to quantify the degree of correlations existing between qubits. In this way the work may give some hints about the problems of generalizing usual entenglement measures from bipartite to multipartite systems.
2022
We focus on characterizing entanglement of high dimensional bipartite states using various statistical correlators for two-qudit mixed states. The salient results obtained are as follows: (a) A scheme for determining the entanglement measure given by Negativity is explored by analytically relating it to the widely used statistical correlators viz. mutual predictability, mutual information and Pearson Correlation coefficient for different types of bipartite arbitrary dimensional mixed states. Importantly, this is demonstrated using only a pair of complementary observables pertaining to the mutually unbiased bases. (b) The relations thus derived provide the separability bounds for detecting entanglement obtained for a fixed choice of the complementary observables, while the bounds per se are state-dependent. Such bounds are compared with the earlier suggested separability bounds. (c) We also show how these statistical correlators can enable distinguishing between the separable, distil...
The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement
2000
We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multi-partite quantum system. This measure, which is based on a generalization of the Schmidt rank of a pure state, is defined on the full state space and is shown to be an entanglement monotone, that is, it cannot increase under local quantum operations with classical communication and under mixing. For a large class of mixed states this measure of entanglement can be calculated exactly, and it provides a detailed classification of mixed states.
Characterizing the entanglement of bipartite quantum systems
Physical Review A, 2003
We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.