State determination: an iterative algorithm

An iterative algorithm for state determination is presented that uses as physical input the probability distributions for the eigenvalues of two or more observables in an unknown state $\Phi$. Starting form an arbitrary state $\Psi_{0}$, a succession of states $\Psi_{n}$ is obtained that converges to $\Phi$ or to a Pauli partner. This algorithm for state reconstruction is efficient and robust as is seen in the numerical tests presented and is a useful tool not only for state determination but also for the study of Pauli partners. Its main ingredient is the Physical Imposition Operator that changes any state to have the same physical properties, with respect to an observable, of another state.Comment: 11 pages 3 figure

Coarse-grained entanglement classification through orthogonal arrays

Classification of entanglement in multipartite quantum systems is an open problem solved so far only for bipartite systems and for systems composed of three and four qubits. We propose here a coarse-grained classification of entanglement in systems consisting of $N$ subsystems with an arbitrary number of internal levels each, based on properties of orthogonal arrays with $N$ columns. In particular, we investigate in detail a subset of highly entangled pure states which contains all states defining maximum distance separable codes. To illustrate the methods presented, we analyze systems of four and five qubits, as well as heterogeneous tripartite systems consisting of two qubits and one qutrit or one qubit and two qutrits.Comment: 38 pages, 1 figur