Bipartite entanglement of quantum states in a pair basis (original) (raw)

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.

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, mixedness, and spin-flip symmetry in multiple-qubit systems

Arxiv preprint quant-ph/ …, 2003

A relationship between a recently introduced multipartite entanglement measure, state mixedness, and spin-flip symmetry is established for any finite number of qubits. It is also shown that, for those classes of states invariant under the spin-flip transformation, there is a complementarity relation between multipartite entanglement and mixedness. A number of example classes of multiple-qubit systems are studied in light of this relationship. PACS numbers: 03.67.-a, 03.65.Ta, 42.79.Ta I. INTRODUCTION.

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.

On bipartite pure-state entanglement structure in terms of disentanglement

Journal of Mathematical Physics, 2006

tation of bipartite state vectors, which is reviewed, and the relevant results of Cassinelli et al. [J. Math. Analys. and Appl., 210, 472 (1997)] in mathematical analysis, which are summed up. Linearly-independent bases (finite or infinite) are shown to be almost as useful in some quantum mechanical studies as orthonormal ones. Finally, it is shown that linearly-independent remote pure-state preparation carries the highest probability of occurrence. This singles out linearly-independent remote influence from all possible ones.

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.

Theoretical and computational aspects of entanglement

2017

We show that the two notions of entanglement: the maximum of the geometric measure of entanglement and the maximum of the nuclear norm is attained for the same states. We affirm the conjecture of Higuchi-Sudberry on the maximum entangled state of four qubits. We introduce the notion of d-density tensor for mixed d-partite states. We show that d-density tensor is separable if and only if its nuclear norm is 111. We suggest an alternating method for computing the nuclear norm of tensors. We apply the above results to symmetric tensors. We give many numerical examples.

Bipartite entanglement measure based on covariances

Physical Review A, 2007

We propose an entanglement measure for two qudits 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 3-concurrence. For mixed states we propose a separability criterion.

Quantification and Scaling of Multipartite Entanglement in Continuous Variable Systems

Physical Review Letters, 2004

We present a theoretical method to determine the multipartite entanglement between different partitions of multimode, fully or partially symmetric Gaussian states of continuous variable systems. For such states, we determine the exact expression of the logarithmic negativity and show that it coincides with that of equivalent two-mode Gaussian states. Exploiting this reduction, we demonstrate the scaling of the multipartite entanglement with the number of modes and its reliable experimental estimate by direct measurements of the global and local purities. 03.67.Mn, 03.65.Ud The full understanding of the structure of multipartite quantum entanglement is a major scope in quantum information theory that is yet to be achieved. At the experimental level, it would be crucial to devise effective strategies to conveniently distribute the entanglement between different parties, depending on the needs of the addressed information protocol. Concerning the theory, the conditions of separability for generic bipartitions of Gaussian states of continuous variable (CV) systems have been derived and analysed [1, 2, 3]. However, the quantification and scaling of entanglement for arbitrary states of multipartite systems remains in general a formidable task . In this work, we present a theoretical scheme to exactly determine the multipartite entanglement of generic Gaussian symmetric states (pure or mixed) of CV systems.