Optical state engineering, quantum communication, and robustness of entanglement promiscuity in three-mode Gaussian states

We present a novel, detailed study on the usefulness of three-mode Gaussian states states for realistic processing of continuous-variable quantum information, with a particular emphasis on the possibilities opened up by their genuine tripartite entanglement. We describe practical schemes to engineer several classes of pure and mixed three-mode states that stand out for their informational and/or entanglement properties. In particular, we introduce a simple procedure -- based on passive optical elements -- to produce pure three-mode Gaussian states with {\em arbitrary} entanglement structure (upon availability of an initial two-mode squeezed state). We analyze in depth the properties of distributed entanglement and the origin of its sharing structure, showing that the promiscuity of entanglement sharing is a feature peculiar to symmetric Gaussian states that survives even in the presence of significant degrees of mixedness and decoherence. Next, we discuss the suitability of the considered tripartite entangled states to the implementation of quantum information and communication protocols with continuous variables. This will lead to a feasible experimental proposal to test the promiscuous sharing of continuous-variable tripartite entanglement, in terms of the optimal fidelity of teleportation networks with Gaussian resources. We finally focus on the application of three-mode states to symmetric and asymmetric telecloning, and single out the structural properties of the optimal Gaussian resources for the latter protocol in different settings. Our analysis aims to lay the basis for a practical quantum communication with continuous variables beyond the bipartite scenario.Comment: 33 pages, 10 figures (some low-res due to size constraints), IOP style; (v2) improved and reorganized, accepted for publication in New Journal of Physic

Harmonics of the AC susceptibility as probes to differentiate the various creep models

We measured the temperature dependence of the 1st and the 3rd harmonics of the AC magnetic susceptibility on some type II superconducting samples at different AC field amplitudes, hAC. In order to interpret the measurements, we computed the harmonics of the AC susceptibility as function of the temperature T, by integrating the non-linear diffusion equation for the magnetic field with different creep models, namely the vortex glass-collective creep (single-vortex, small bundle and large bundle) and Kim-Anderson model. We also computed them by using a non-linear phenomenological I-V characteristics, including a power law dependence of the pinning potential on hAC. Our experimental results were compared with the numerically computed ones, by the analysis of the Cole-Cole plots. This method results more sensitive than the separate component analysis, giving the possibility to obtain detailed information about the contribution of the flux dynamic regimes in the magnetic response of the analysed samples.Comment: 9 pages, 6 figures, submitted to Physica

Theory of ground state factorization in quantum cooperative systems

We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows to determine rigorously existence, location, and exact form of separable ground states in a large variety of, generally non-exactly solvable, spin models belonging to different universality classes. The theory applies to translationally invariant systems, irrespective of spatial dimensionality, and for spin-spin interactions of arbitrary range.Comment: 4 pages, 1 figur

Controllable Gaussian-qubit interface for extremal quantum state engineering

We study state engineering through bilinear interactions between two remote qubits and two-mode Gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode Gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode Gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios.Comment: 4+3 pages, 6 figures, RevTeX4. Close to published version with appendi

Identification of the vortex glass phase by harmonics of the AC magnetic susceptibility

We compared the AC magnetic susceptibility behaviour for the vortex glass phase and for the creep phenomena with an inhomogeneous pinning potential. The temperature dependence of the harmonics of the susceptibility have been numerically simulated with these two models, and we studied them as a function of the frequency, in terms of Cole-Cole plots. From our analysis we show that it is possible to distinguish between the two different phases, because of their clear differences in the Cole-Cole plots behaviour with the frequency.Comment: 8 pages, 2 figures to be published on "The Journal of Physics and Chemistry of Solids

Entanglement quantification by local unitaries

Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitaries play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as "mirror entanglement". They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary. To the action of each different local unitary there corresponds a different distance. We then minimize these distances over the sets of local unitaries with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary for the associated mirror entanglement to be faithful, i.e. to vanish on and only on separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the "stellar mirror entanglement" associated to traceless local unitaries with nondegenerate spectrum and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of [Giampaolo and Illuminati, Phys. Rev. A 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension, and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.Comment: 13 pages, 3 figures. Improved and generalized proof of monotonicity of the mirror and stellar entanglemen

Optical implementation and entanglement distribution in Gaussian valence bond states

We study Gaussian valence bond states of continuous variable systems, obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites, applied at each of $N$ sites of an harmonic chain. The entanglement distribution in Gaussian valence bond states can be controlled by varying the input amount of entanglement engineered in a (2M+1)-mode Gaussian state known as the building block, which is isomorphic to the projector applied at a given site. We show how this mechanism can be interpreted in terms of multiple entanglement swapping from the chain of ancillary bonds, through the building blocks. We provide optical schemes to produce bisymmetric three-mode Gaussian building blocks (which correspond to a single bond, M=1), and study the entanglement structure in the output Gaussian valence bond states. The usefulness of such states for quantum communication protocols with continuous variables, like telecloning and teleportation networks, is finally discussed.Comment: 15 pages, 6 figures. To appear in Optics and Spectroscopy, special issue for ICQO'2006 (Minsk). This preprint contains extra material with respect to the journal versio

Entanglement, Purity, and Information Entropies in Continuous Variable Systems

Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal ({\em i.e.}referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information about the state makes it impossible to distinguish between quantum and classical correlations. Here we show how the joint knowledge of the global and marginal degrees of information of a quantum state, quantified by the purities or in general by information entropies, provides an accurate characterization of its entanglement. In particular, for Gaussian states of continuous variable systems, we classify the entanglement of two--mode states according to their degree of total and partial mixedness, comparing the different roles played by the purity and the generalized $p-$entropies in quantifying the mixedness and bounding the entanglement. We prove the existence of strict upper and lower bounds on the entanglement and the existence of extremally (maximally and minimally) entangled states at fixed global and marginal degrees of information. This results allow for a powerful, operative method to measure mixed-state entanglement without the full tomographic reconstruction of the state. Finally, we briefly discuss the ongoing extension of our analysis to the quantification of multipartite entanglement in highly symmetric Gaussian states of arbitrary $1 \times N$-mode partitions.Comment: 16 pages, 5 low-res figures, OSID style. Presented at the International Conference ``Entanglement, Information and Noise'', Krzyzowa, Poland, June 14--20, 200

Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states

We address the estimation of the loss parameter of a bosonic channel probed by arbitrary signals. Unlike the optimal Gaussian probes, which can attain the ultimate bound on precision asymptotically either for very small or very large losses, we prove that Fock states at any fixed photon number saturate the bound unconditionally for any value of the loss. In the relevant regime of low-energy probes, we demonstrate that superpositions of the first low-lying Fock states yield an absolute improvement over any Gaussian probe. Such few-photon states can be recast quite generally as truncations of de-Gaussified photon-subtracted states.Comment: 4 pages, 3 figure