Deterministic Plug-and-Play for Quantum Communication

We present a scheme for secure deterministic quantum communication without using entanglement, in a Plug-and-Play fashion. The protocol is completely deterministic, both in the encoding procedure and in the control one, thus doubling the communication rate with respect to other setups; moreover, deterministic nature of transmission, apart from rendering unnecessary bases revelation on the public channel, allows the realization of protocols like `direct communication' and `quantum dialogue'. The encoding exploits the phase degree of freedom of a photon, thus paving the way to an optical fiber implementation, feasible with present day technology.Comment: 4 pages, 2 figures; one reference update

Schwinger's Picture of Quantum Mechanics IV: Composition and independence

The groupoids description of Schwinger's picture of quantum mechanics is continued by discussing the closely related notions of composition of systems, subsystems, and their independence. Physical subsystems have a neat algebraic description as subgroupoids of the Schwinger's groupoid of the system. The groupoids picture offers two natural notions of composition of systems: Direct and free products of groupoids, that will be analyzed in depth as well as their universal character. Finally, the notion of independence of subsystems will be reviewed, finding that the usual notion of independence, as well as the notion of free independence, find a natural realm in the groupoids formalism. The ideas described in this paper will be illustrated by using the EPRB experiment. It will be observed that, in addition to the notion of the non-separability provided by the entangled state of the system, there is an intrinsic `non-separability' associated to the impossibility of identifying the entangled particles as subsystems of the total system.Comment: 32 pages. Comments are welcome

Covariant Variational Evolution and Jacobi Brackets: Fields

The analysis of the covariant brackets on the space of functions on the solutions to a variational problem in the framework of contact geometry initiated in the companion letter Ref.19 is extended to the case of the multisymplectic formulation of the free Klein-Gordon theory and of the free Schr\"{o}dinger equation.Comment: 16 page

Covariant Jacobi Brackets for Test Particles

We show that the space of observables of test particles carries a natural Jacobi structure which is manifestly invariant under the action of the Poincar\'{e} group. Poisson algebras may be obtained by imposing further requirements. A generalization of Peierls procedure is used to extend this Jacobi bracket on the space of time-like geodesics on Minkowski space-time.Comment: 13 pages Submitted to MPL

Quantum dynamics of a high-finesse optical cavity coupled with a thin semi-transparent membrane

We study the quantum dynamics of the cavity optomechanical system formed by a Fabry-Perot cavity with a thin vibrating membrane at its center. We first derive the general multimode Hamiltonian describing the radiation pressure interaction between the cavity modes and the vibrational modes of the membrane. We then restrict the analysis to the standard case of a single cavity mode interacting with a single mechanical resonator and we determine to what extent optical absorption by the membrane hinder reaching a quantum regime for the cavity-membrane system. We show that membrane absorption does not pose serious limitations and that one can simultaneously achieve ground state cooling of a vibrational mode of the membrane and stationary optomechanical entanglement with state-of-the-art apparatuses.Comment: 14 pages, 7 figure

Agreement in epidemic data aggregation

Computing and spreading global information in large-scale distributed systems pose significant challenges when scalability, parallelism, resilience and consistency are demanded. Epidemic protocols are a robust and scalable computing and communication paradigm that can be effectively used for information dissemination and data aggregation in a fully decentralised context where each network node requires the local computation of a global synopsis function. Theoretical analysis of epidemic protocols for synchronous and static network models provide guarantees on the convergence to a global target and on the consistency among the network nodes. However, practical applications in real-world networks may require the explicit detection of both local convergence and global agreement (consensus). This work introduces the Epidemic Consensus Protocol (ECP) for the determination of consensus on the convergence of a decentralised data aggregation task. ECP adopts a heuristic method to locally detect convergence of the aggregation task and stochastic phase transitions to detect global agreement and reach consensus. The performance of ECP has been investigated by means of simulations and compared to a tree-based Three-Phase Commit protocol (3PC). Although, as expected, ECP exhibits total communication costs greater than the optimal tree-based protocol, it is shown to have better performance and scalability properties; ECP can achieve faster convergence to consensus for large system sizes and inherits the intrinsic decentralisation, fault-tolerance and robustness properties of epidemic protocols

The Elephant Quantum Walk

We explore the impact of long-range memory on the properties of a family of quantum walks in a one-dimensional lattice and discrete time, which can be understood as the quantum version of the classical "Elephant Random Walk" non-Markovian process. This Elephant Quantum Walk is robustly superballistic with the standard deviation showing a constant exponent, $\sigma \propto t^{3/ 2}$ , whatever the quantum coin operator, on which the diffusion coefficient is dependent. On the one hand, this result indicates that contrarily to the classical case, the degree of superdiffusivity in quantum non- Markovian processes of this kind is mainly ruled by the extension of memory rather than other microscopic parameters that explicitly define the process. On the other hand, these parameters reflect on the diffusion coefficient.Comment: 4 figures, any comments is welcome. Accepted in PR

Dynamical aspects in the Quantizer-Dequantizer formalism

The use of the quantizer-dequantizer formalism to describe the evolution of a quantum system is reconsidered. We show that it is possible to embed a manifold in the space of quantum states of a given auxiliary system by means of an appropriate quantizer-dequantizer system. If this manifold of states is invariant with respect to some unitary evolution, the quantizer-dequantizer system provides a classical-like realization of such dynamics, which in general is non linear. Integrability properties are also discussed. Weyl systems and generalized coherente states are used as a simple illustration of these ideas.Comment: 15 page

Aspects of geodesical motion with Fisher-Rao metric: classical and quantum

The purpose of this article is to exploit the geometric structure of Quantum Mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that the end points of geodesics in the classical setting coincide with the probability distributions that minimise Shannon's Entropy, i.e. with distributions of zero dispersion. In the quantum setting this happens only for particular initial conditions, which in turn correspond to classical submanifolds. This result can be interpreted as a geometric manifestation of the uncertainty principle.Comment: 15 pages, 5 figure