Inference and learning in sparse systems with multiple states

We discuss how inference can be performed when data are sampled from the non-ergodic phase of systems with multiple attractors. We take as model system the finite connectivity Hopfield model in the memory phase and suggest a cavity method approach to reconstruct the couplings when the data are separately sampled from few attractor states. We also show how the inference results can be converted into a learning protocol for neural networks in which patterns are presented through weak external fields. The protocol is simple and fully local, and is able to store patterns with a finite overlap with the input patterns without ever reaching a spin glass phase where all memories are lost.Comment: 15 pages, 10 figures, to be published in Phys. Rev.

Squeezing as an irreducible resource

We show that squeezing is an irreducible resource which remains invariant under transformations by linear optical elements. In particular, we give a decomposition of any optical circuit with linear input-output relations into a linear multiport interferometer followed by a unique set of single mode squeezers and then another multiport interferometer. Using this decomposition we derive a no-go theorem for superpositions of macroscopically distinct states from single-photon detection. Further, we demonstrate the equivalence between several schemes for randomly creating polarization-entangled states. Finally, we derive minimal quantum optical circuits for ideal quantum non-demolition coupling of quadrature-phase amplitudes.Comment: 4 pages, 3 figures, new title, removed the fat

Bell Measurements and Observables

A general matrix approach to study entangled states is presented, based on operator completeness relations. Bases of unitary operators are considered, with focus on irreducible representations of groups. Bell measurements for teleportation are considered, and robustness of teleportation to various kinds of non idealities is shown.Comment: 11 pages. Elsart styl

Collaboration in Social Networks

The very notion of social network implies that linked individuals interact repeatedly with each other. This allows them not only to learn successful strategies and adapt to them, but also to condition their own behavior on the behavior of others, in a strategic forward looking manner. Game theory of repeated games shows that these circumstances are conducive to the emergence of collaboration in simple games of two players. We investigate the extension of this concept to the case where players are engaged in a local contribution game and show that rationality and credibility of threats identify a class of Nash equilibria -- that we call "collaborative equilibria" -- that have a precise interpretation in terms of sub-graphs of the social network. For large network games, the number of such equilibria is exponentially large in the number of players. When incentives to defect are small, equilibria are supported by local structures whereas when incentives exceed a threshold they acquire a non-local nature, which requires a "critical mass" of more than a given fraction of the players to collaborate. Therefore, when incentives are high, an individual deviation typically causes the collapse of collaboration across the whole system. At the same time, higher incentives to defect typically support equilibria with a higher density of collaborators. The resulting picture conforms with several results in sociology and in the experimental literature on game theory, such as the prevalence of collaboration in denser groups and in the structural hubs of sparse networks

Multiple membrane cavity optomechanics

We investigate theoretically the extension of cavity optomechanics to multiple membrane systems. We describe such a system in terms of the coupling of the collective normal modes of the membrane array to the light fields. We show these modes can be optically addressed individually and be cooled, trapped and characterized, e.g. via quantum nondemolition measurements. Analogies between this system and a linear chain of trapped ions or dipolar molecules imply the possibility of related applications in the quantum regime.Comment: 4 pages, 2 figure

Optimal fidelity of teleportation of coherent states and entanglement

We study the Braunstein-Kimble protocol for the continuous variable teleportation of a coherent state. We determine lower and upper bounds for the optimal fidelity of teleportation, maximized over all local Gaussian operations for a given entanglement of the two-mode Gaussian state shared by the sender (Alice) and the receiver (Bob). We also determine the optimal local transformations at Alice and Bob sites and the corresponding maximum fidelity when one restricts to local trace-preserving Gaussian completely positive maps.Comment: 10 pages, 2 figure

Optical implementation of continuous-variable quantum cloning machines

We propose an optical implementation of the Gaussian continuous-variable quantum cloning machines. We construct a symmetric N -> M cloner which optimally clones coherent states and we also provide an explicit design of an asymmetric 1 -> 2 cloning machine. All proposed cloning devices can be built from just a single non-degenerate optical parametric amplifier and several beam splitters.Comment: 4 pages, 3 figures, REVTe