Numerical evaluation of convex-roof entanglement measures with applications to spin rings

  title={Numerical evaluation of convex-roof entanglement measures with applications to spin rings},
  author={Beat Rothlisberger and Jorg Lehmann and Daniel Loss},
  journal={Physical Review A},
We present two ready-to-use numerical algorithms to evaluate convex-roof extensions of arbitrary pure-state entanglement monotones. Their implementation leaves the user merely with the task of calculating derivatives of the respective pure-state measure. We provide numerical tests of the algorithms and demonstrate their good convergence properties. We further employ them in order to investigate the entanglement in particular few-spins systems at finite temperature. Namely, we consider… 

Figures from this paper

A geometric comparison of entanglement and quantum nonlocality in discrete systems

We compare entanglement with quantum nonlocality employing a geometric structure of the state space of bipartite qudits. The central object is a regular simplex spanned by generalized Bell states.

Convex-roof entanglement measures of density matrices block diagonal in disjoint subspaces for the study of thermal states

We provide a proof that entanglement of any density matrix which block diagonal in subspaces which are disjoint in terms of the Hilbert space of one of the two potentially entangled subsystems can


. Many entanglement measures are first defined for pure states of a bipartite Hilbert space, and then extended to mixed states via the convex roof extension. In this article we alter the convex roof

Numerical and analytical results for geometric measure of coherence and geometric measure of entanglement

A semidefinite algorithm is provided to numerically calculate geometric measure of coherence for arbitrary finite-dimensional mixed states and some special kinds of higher dimensional mixed states, and an analytical solution is obtained for a special kind of mixed states.

Variational Quantum Algorithm for Approximating Convex Roofs

Many entanglement measures are first defined for pure states of a bipartite Hilbert space, and then extended to mixed states via the convex roof extension. In this article we alter the convex roof

Multipartite quantum entanglement evolution in photosynthetic complexes.

The hypothesis that entanglement is maximum primary along the two distinct electronic energy transfer pathways is supported and monogamy is used to give a lower bound and an upper bound from the evaluation of the convex roof.

libCreme: An optimization library for evaluating convex-roof entanglement measures

Quantum entanglement in finite-dimensional Hilbert spaces

In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its

Multipartite entanglement and few-body Hamiltonians

We investigate the possibility to obtain higly multipartite-entangled states as non-degenerate eigenstates of Hamiltonians that involve only short-range and few-body interactions. We study small-size

Measurement-induced nonlocality in arbitrary dimensions in terms of the inverse approximate joint diagonalization

Here we focus on the measurement induced nonlocality and present a redefinition in terms of the skew information subject to a broken observable. It is shown that the obtained quantity possesses an



Variational characterizations of separability and entanglement of formation

In this paper we develop a mathematical framework for the characterization of separability and entanglement of formation (EOF) of general bipartite states. These characterizations are variational in

An introduction to entanglement measures

The theory of entanglement measures is reviewed, concentrating mostly on the finite dimensional two-party case, and an exteneive list of open research questione will be presented.

Quantitative entanglement witnesses

All these tests—based on the very same data—give rise to quantitative estimates in terms of entanglement measures, and if a test is strongly violated, one can also infer that the state was quantitatively very much entangled, in the bipartite and multipartite setting.

Highly entangled ground States in tripartite qubit systems.

By generalizing a conjugate gradient optimization algorithm originally developed to evaluate the entanglement of formation, it is demonstrated that tau can be calculated efficiently and with high precision.


This work reviews and extends recent results concerning the distribution of entanglement, as well as nonlocality (in terms of inequality violations) in tripartite qubit systems. With recourse to a

Entangled three-qubit states without concurrence and three-tangle.

By studying the Coffman-Kundu-Wootters inequality, it is found that, while the amounts of inequivalent entanglement types strictly add up for pure states, this "monogamy" can be lifted for mixed states by virtue of vanishing tangle measures.

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 average

Entanglement-based quantum communication over 144km

Quantum entanglement is the main resource to endow the field of quantum information processing with powers that exceed those of classical communication and computation. In view of applications such

Relation between entanglement measures and Bell inequalities for three qubits

For two qubits in a pure state there exists a one-to-one relation between the entanglement measure (the concurrence C) and the maximal violation M of a Bell inequality. No such relation exists for

Three qubits can be entangled in two inequivalent ways

Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single