Optimal Decompositions of Barely Separable States

Two families of bipartite mixed quantum states are studied for which it is proved that the number of members in the optimal-decomposition ensemble --- the ensemble realizing the entanglement of formation --- is greater than the rank of the mixed state. We find examples for which the number of states in this optimal ensemble can be larger than the rank by an arbitrarily large factor. In one case the proof relies on the fact that the partial transpose of the mixed state has zero eigenvalues; in the other case the result arises from the properties of product bases that are completable only by embedding in a larger Hilbert space.Comment: 14 Pages (RevTeX), 1 figure (eps). Submitted to the special issue of the J. Mod. Opt. V2: Change in terminology from "ensemble length" to "ensemble cardinality

Broken Symmetries in the Entanglement of Formation

We compare some recent computations of the entanglement of formation in quantum information theory and of the entropy of a subalgebra in quantum ergodic theory. Both notions require optimization over decompositions of quantum states. We show that both functionals are strongly related for some highly symmetric density matrices. We discuss the presence of broken symmetries in relation with the structure of the optimal decompositions.Comment: 21 pages, LateX, no figure

Gaussian Entanglement of Formation

We introduce a Gaussian version of the entanglement of formation adapted to bipartite Gaussian states by considering decompositions into pure Gaussian states only. We show that this quantity is an entanglement monotone under Gaussian operations and provide a simplified computation for states of arbitrary many modes. For the case of one mode per site the remaining variational problem can be solved analytically. If the considered state is in addition symmetric with respect to interchanging the two modes, we prove additivity of the considered entanglement measure. Moreover, in this case and considering only a single copy, our entanglement measure coincides with the true entanglement of formation.Comment: 8 pages (references updated, typos corrected

Linking a distance measure of entanglement to its convex roof

An important problem in quantum information theory is the quantification of entanglement in multipartite mixed quantum states. In this work, a connection between the geometric measure of entanglement and a distance measure of entanglement is established. We present a new expression for the geometric measure of entanglement in terms of the maximal fidelity with a separable state. A direct application of this result provides a closed expression for the Bures measure of entanglement of two qubits. We also prove that the number of elements in an optimal decomposition w.r.t. the geometric measure of entanglement is bounded from above by the Caratheodory bound, and we find necessary conditions for the structure of an optimal decomposition.Comment: 11 pages, 4 figure

Entanglement of 2xK quantum systems

We derive an analytical expression for the lower bound of the concurrence of mixed quantum states of composite 2xK systems. In contrast to other, implicitly defined entanglement measures, the numerical evaluation of our bound is straightforward. We explicitly evaluate its tightness for general mixed states of 2x3 systems, and identify a large class of states where our expression gives the exact value of the concurrence.Comment: 7 pages, 1 figure, to be published in Europhysics Lette

Minimally Entangled Typical Thermal State Algorithms

We discuss a method based on sampling minimally entangled typical thermal states (METTS) that can simulate finite temperature quantum systems with a computational cost comparable to ground state DMRG. Detailed implementations of each step of the method are presented, along with efficient algorithms for working with matrix product states and matrix product operators. We furthermore explore how properties of METTS can reveal characteristic order and excitations of systems and discuss why METTS form an efficient basis for sampling. Finally, we explore the extent to which the average entanglement of a METTS ensemble is minimal.Comment: 18 pages, 14 figure