Multiqubit systems: highly entangled states and entanglement distribution

Abstract

A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multiqubits states. In particular, our present results are compared with those recently reported by Brown et al (J. Phys. A: Math. Gen. 2005 38 1119). The statistical distribution of entanglement values for the aforementioned multiqubit systems is also explored.

q-entropies and the entanglement dynamics of two-qubits interacting with an environment

“…In part this is due to the fact that to evaluate these entropies it is not necessary to diagonalize the density matrix. The q-entropic measure S (T ) 2 [ρ] is usually referred to as the linear entropy of the density matrix ρ in the literature, and has proven to be very useful in the field of quantum information theory (see [37,38] and references therein). Furthermore, as already explained, the entropic difference D (T ) 2 is closely related to a recently advanced experimentally measurable entanglement indicator [33].…”

Highly entangled multi-qubit states with simple algebraic structure

“…Properties for a good entanglement measure are reviewed and discussed in [8,9,15]. An alternative to the analytic approach was presented by Brown et al [4] and later by Borras et al [1]. Both works explore the application of numerical optimisation techniques to search for highly entangled multi-qubit states.…”

“…In the work of Borras et al [1], the search is restricted to pure states of 4, 5, 6 and 7 qubits, and several measures of entanglement are investigated. The overall search algorithm is very similar to the hill-climbing scheme employed by Brown et al , and the authors also explore the statistical distribution of entanglement for systems of the sizes aforementioned.…”

“…Recent works by Brown et al [4] and Borras et al [1] have explored numerical optimisation procedures to search for highly entangled multi-qubit states according to some computationally tractable entanglement measure. We present an alternative scheme based upon the idea of searching for states having not only high entanglement but also simple algebraic structure.…”

Efficient generation of random multipartite entangled states using time-optimal unitary operations

“…Although a large amount of different multipartite entanglement measures has recently been proposed, a considerable amount of research has particularly been devoted to the study of multiqubit entanglement measures defined as the sum of bipartite entanglement measures over all (or an appropriate family of) the possible bipartitions of the full system [10,11,12,13,14]. There exist two popular entanglement measures for multiqubit pure states, one based on the von Neumann entropy of marginal density matrices and the other one based upon * toni.borras@uib.es † ana.majtey@uib.es ‡ montse.casas@uib.es the linear entropy of those matrices.…”