Roberto Floreanini

Environment induced entanglement in Markovian dissipative dynamics.

We show that two, noninteracting two-level systems, immersed in a common bath, can become mutually entangled when evolving according to a Markovian, completely positive reduced dynamics.

q-Orthogonal polynomials and the oscillator quantum group

The oscillator quantum algebra is shown to provide a group-theoretic setting for the q-Laguerre and q-Hermite polynomials.

OPEN QUANTUM DYNAMICS: COMPLETE POSITIVITY AND ENTANGLEMENT

We review the standard treatment of open quantum systems in relation to quantum entanglement, analyzing, in particular, the behavior of bipartite systems immersed in the same environment. We first focus upon the notion of complete positivity, a physically motivated algebraic constraint on the quantum dynamics, in relation to quantum entanglement, i.e. the existence of statistical correlations which can not be accounted for by classical probability. We then study the entanglement power of heat baths versus their decohering properties, a topic of increasing importance in the framework of the fast developing fields of quantum information, communication and computation. The presentation is self contained and, through several examples, it offers a detailed survey of the physics and of the most relevant and used techniques relative to both quantum open system dynamics and quantum entanglement.

More on the q-oscillator algebra and q-orthogonal polynomials

Properties of certain q-orthogonal polynomials are connected to the q-oscillator algebra. The Wall and q-Laguerre polynomials are shown to arise as matrix elements of q-exponentials of the generators in a representation of this algebra. A realization is presented where the continuous q-Hermite polynomials form a basis of the representation space. Various identities are interpreted within this model. In particular, the connection formula between the continuous big q-Hermite and the continuous q-Hermite polynomials is thus obtained, and two generating functions for these last polynomials are derived algebraically.

Lie symmetries of finite‐difference equations

Discretizations of the Helmholtz, heat, and wave equations on uniform lattices are considered in various space–time dimensions. The symmetry properties of these finite‐difference equations are determined and it is found that they retain the same Lie symmetry algebras as their continuum limits. Solutions with definite transformation properties are obtained; identities and formulas for these functions are then derived using the symmetry algebra.

On the defining relations of quantum superalgebras

In defining quantum superalgebras, extra relations need to be added to the Serre-like relations. They are obtained for slq(m, n) and ospq(m, 2n) usingq-oscillator representations.

Open system approach to neutrino oscillations

Neutrino oscillations are studied in the general framework of open quantum systems by means of extended dynamics that take into account possible dissipative effects. These new phenomena induce modifications in the neutrino oscillation pattern that in general can be parametrized by means of six phenomenological constants. Although very small, stringent bounds on these parameters are likely to be given by future planned neutrino experiments.

q-analogues of the parabose and parafermi oscillators and representations of quantum algebras

Deformations of the one-dimensional parabose oscillators are presented. They are shown to provide Fock representations of the quantum sp q(2) algebra and ospq(1, 2) superalgebra. The representations of suq(2) are used to define the q-analogues of the parafermi oscillators.

On the quantum group and quantum algebra approach toq-special functions

Two interpretations ofq-special functions based on quantum groups and algebras have been presented in the literature. The connection between these approaches is explained using as an example the case whereUq(sl(2)) is the basic structure.

Entanglement and squeezing with identical particles: ultracold atom quantum metrology

By identifying non-local effects in systems of identical Bosonic qubits through correlations of their commuting observables, we show that entanglement is not necessary to violate certain squeezing inequalities that hold for distinguishable qubits and that spin squeezing may not be necessary to achieve sub-shot noise accuracies in ultra-cold atom interferometry.In quantum metrological applications based on ultracold atom systems, entangled initial states are thought necessary to achieve sub-shot-noise accuracies. This conclusion, although strictly true for systems of distinguishable particles, does no longer hold for systems of identical particles. Indeed, while quantum non-locality is necessary, it can be encoded into the interferometric apparatus and not into the initial states. In particular, no preliminary spin-squeezing is necessary to reach quantum performances in metrological applications of ultracold atom physics.