Purification and correlated measurements of bipartite mixed states

We prove that all purifications of a non-factorable state (i.e., the state which cannot be expressed in a form $\rho_{AB}=\rho_A\otimes\rho_B$) are entangled. We also show that for any bipartite state there exists a pair of measurements which are correlated on this state if and only if the state is non-factorable.Comment: 4 revtex pages, to appear in Phys. Rev.

Global-fidelity limits of state-dependent cloning of mixed states

By relevant modifications, the known global-fidelity limits of state-dependent cloning are extended to mixed quantum states. We assume that the ancilla contains some a priori information about the input state. As it is shown, the obtained results contribute to the stronger no-cloning theorem. An attainability of presented limits is discussed.Comment: 8 pages, ReVTeX, 1 figure. In revised form an attainability of presented limits is discussed. Detected errors are corrected. Elucidative figure is added. Minor grammatical changes are made. More explanation

A Geometric Picture of Entanglement and Bell Inequalities

We work in the real Hilbert space H_s of hermitian Hilbert-Schmid operators and show that the entanglement witness which shows the maximal violation of a generalized Bell inequality (GBI) is a tangent functional to the convex set S subset H_s of separable states. This violation equals the euclidean distance in H_s of the entangled state to S and thus entanglement, GBI and tangent functional are only different aspects of the same geometric picture. This is explicitly illustrated in the example of two spins, where also a comparison with familiar Bell inequalities is presented.Comment: 17 pages, 5 figures, 4 references adde

Entanglement Measures under Symmetry

We show how to simplify the computation of the entanglement of formation and the relative entropy of entanglement for states, which are invariant under a group of local symmetries. For several examples of groups we characterize the state spaces, which are invariant under these groups. For specific examples we calculate the entanglement measures. In particular, we derive an explicit formula for the entanglement of formation for UU-invariant states, and we find a counterexample to the additivity conjecture for the relative entropy of entanglement.Comment: RevTeX,16 pages,9 figures, reference added, proof of monotonicity corrected, results unchange

Disentanglement and Inseparability correlation : in two-qubit system

Started from local universal isotropic disentanglement, a threshold inequality on reduction factors is proposed, which is necessary and sufficient for this type of disentanglement processes. Furthermore, we give the conditions realizing ideal disentanglement processes provided that some information on quantum states is known. In addition, based on fully entangled fraction, a concept called inseparability correlation is presented. Some properties on inseparability correlation coefficient are studied.Comment: 10 Pages, 2 Figures, REVTeX; to appear in PR

Entanglement, Mixedness, and Spin-Flip Symmetry in Multiple-Qubit Systems

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, within 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.Comment: To appear in Physical Review A; submitted 14 May 200

A Generalization of Quantum Stein's Lemma

We present a generalization of quantum Stein's Lemma to the situation in which the alternative hypothesis is formed by a family of states, which can moreover be non-i.i.d.. We consider sets of states which satisfy a few natural properties, the most important being the closedness under permutations of the copies. We then determine the error rate function in a very similar fashion to quantum Stein's Lemma, in terms of the quantum relative entropy. Our result has two applications to entanglement theory. First it gives an operational meaning to an entanglement measure known as regularized relative entropy of entanglement. Second, it shows that this measure is faithful, being strictly positive on every entangled state. This implies, in particular, that whenever a multipartite state can be asymptotically converted into another entangled state by local operations and classical communication, the rate of conversion must be non-zero. Therefore, the operational definition of multipartite entanglement is equivalent to its mathematical definition.Comment: 30 pages. (see posting by M. Piani arXiv:0904.2705 for a different proof of the strict positiveness of the regularized relative entropy of entanglement on every entangled state). published version

Quantum optics in the phase space - A tutorial on Gaussian states

In this tutorial, we introduce the basic concepts and mathematical tools needed for phase-space description of a very common class of states, whose phase properties are described by Gaussian Wigner functions: the Gaussian states. In particular, we address their manipulation, evolution and characterization in view of their application to quantum information.Comment: Tutorial. 23 pages, 1 figure. Updated version accepted for publication in EPJ - ST devoted to the memory of Federico Casagrand

Equation of motion for entanglement

We review an evolution equation for quantum entanglement for 2x2 dimensional quantum systems, the smallest system that can exhibit entanglement, and extend it to higher dimensional systems. Furthermore, we provide statistical evidence for the equation's applicability to the experimentally relevant domain of weakly mixed states.Comment: 7 pages, 3 figures, published versio

CVD diamond coated silicon nitride self-mated systems : tribological behaviour under high loads

Friction and wear behaviour of self-mated chemical vapour deposited (CVD) diamond films coating silicon nitride ceramics (Si3N4) were investigated in ambient atmosphere. The tribological tests were conducted in a reciprocal motion ball-on-flat type tribometer under applied normal loads up to 80 N (~10 GPa). Several characterisation techniques - including scanning electron microscopy (SEM), atomic force microscopy (AFM) and micro-Raman studies - were used in order to assess the quality, stress state and wear resistance of the coatings. In addition, a novel method is presented to estimate the wear coefficient of the diamond coated flat specimens from AFM and optical microscopy (OM) observations of the wear tracks