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F. Benatti

Publications and source records attributed to F. Benatti.

At least 55 records · Page 3Linked to original sources
arXiv2007

Redfield reduced dynamics and entanglement

In phenomenological applications the time evolution of subsystems immersed in an external environment are sometimes described by Markovian semigroups of Redfield type that result non-positive: the appearence of negative probabilities is avoided by restricting the admissible initial conditions to those states that remain positive under the action of the dynamics. We show that this often adopted procedure may lead to physical inconsistencies in presence of entanglement.

quant-ph↗
arXiv2006

Slipped non-Positive Reduced Dynamics and Entanglement

Non-positive Markov approximations are sometimes used to describe the dynamics of qubits in weak interaction with suitable environments; the appearance of negative probabilities is avoided by assuming that the transient regime eliminates from the possible initial conditions those qubit states which would otherwise be mapped out of the Bloch sphere by the subsequent Markovian time-evolution. By means of a simple model, we discuss some physical inconsistencies of this approach in relation to entanglement; in particular, we show that slipped non-positive reduced dynamics might create entanglement through a purely local action.

quant-ph↗
arXiv2006

Tests of Complete Positivity in Fiber Optics

We consider the propagation of polarized photons in optical fibers under the action of randomly generated noise. In such situation, the change in time of the photon polarization can be described by a quantum dynamical semigroup. We show that the hierarchy among the decay constants of the polarization density matrix elements as prescribed by complete positivity can be experimentally probed using standard laboratory set-ups.

quant-ph↗
arXiv2006

Asymptotic Entanglement of Two Independent Systems in a Common Bath

Two, non-interacting systems immersed in a common bath and evolving with a Markovian, completely positive dynamics can become initially entangled via a purely noisy mechanism. Remarkably, for certain, phenomenologically relevant environments, the quantum correlations can persist even in the asymptotic long-time regime.

quant-ph↗
arXiv2006

Discrete Dynamical Systems Embedded in Cantor Sets

While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $ N $ variables, as binary neural networks and cellular automata. The main difficulty is the choice of a suitable topology to study the limit $N\to\infty$. By embedding the discrete phase space into a Cantor set we provided a natural setting to define topological entropy and Lyapunov exponents through the concept of error-profile. We made explicit calculations both numerical and analytic for well known discrete dynamical models.

nlin.CD↗
arXiv2006

Entangling oscillators through environment noise

We consider two independent bosonic oscillators immersed in a common bath, evolving in time with a completely positive, markovian, quasi-free (Gaussian) reduced dynamics. We show that an initially separated Gaussian state can become entangled as a result of a purely noisy mechanism. In certain cases, the dissipative dynamics allows the persistence of these bath induced quantum correlations even in the asymptotic equilibrium state.

quant-ph↗
arXiv2005

Controlling Entanglement Generation in External Quantum Fields

Two, non-interacting two-level atoms immersed in a common bath can become mutually entangled when evolving with a Markovian, completely positive dynamics. For an environment made of external quantum fields, this phenomenon can be studied in detail: one finds that entanglement production can be controlled by varying the bath temperature and the distance between the atoms. Remarkably, in certain circumstances, the quantum correlations can persist in the asymptotic long-time regime.

quant-ph↗
arXiv2005

Multi-distributed Entanglement in Finitely Correlated Chains

The entanglement-sharing properties of an infinite spin-chain are studied when the state of the chain is a pure, translation-invariant state with a matrix-product structure. We study the entanglement properties of such states by means of their finitely correlated structure. These states are recursively constructed by means of an auxiliary density matrix ρon a matrix algebra B and a completely positive map E: A \otimes B -> B, where A is the spin 2\times 2 matrix algebra. General structural results for the infinite chain are therefore obtained by explicit calculations in (finite) matrix algebras. In particular, we study not only the entanglement shared by nearest-neighbours, but also, differently from previous works, the entanglement shared between connected regions of the spin-chain. This range of possible applications is illustrated and the maximal concurrence C=1/\sqrt{2} for the entanglement of connected regions can actually be reached.

quant-ph↗
arXiv2005

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 behaviour of bipartite systems immersed in a 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.

quant-ph↗
arXiv2004

Dissipative neutrino oscillations in randomly fluctuating matter

The generalized dynamics describing the propagation of neutrinos in randomly fluctuating media is analyzed: it takes into account matter-induced, decoherence phenomena that go beyond the standard MSW effect. A widely adopted density fluctuation pattern is found to be physically untenable: a more general model needs to be instead considered, leading to flavor changing effective neutrino-matter interactions. They induce new, dissipative effects that modify the neutrino oscillation pattern in a way amenable to a direct experimental analysis.

hep-ph↗
arXiv2004

Entanglement generation in the Unruh effect

The master equation describing the completely positive time evolution of a uniformly accelerated two-level system in weak interaction with a scalar field in the Minkowski vacuum is derived and explicitly solved. It encodes the well known Unruh effect, leading to a purely thermal equilibrium state. This asymptotic state turns out to be entangled when the uniformly accelerating system is composed by two, independent two-level atoms.

quant-ph↗
arXiv2004

Quantum dynamical semigroups and non-decomposable positive maps

We study dynamical semigroups of positive, but not completely positive maps on finite-dimensional bipartite systems and analyze properties of their generators in relation to non-decomposability and bound-entanglement. An example of non-decomposable semigroup leading to a 4x4-dimensional bound-entangled density matrix is explicitly obtained.

quant-ph↗
arXiv2004

Classical Limit of Quantum Dynamical Entropies

Two non-commutative dynamical entropies are studied in connection with the classical limit. For systems with a strongly chaotic classical limit, the Kolmogorov-Sinai invariant is recovered on time scales that are logarithmic in the quantisation parameter. The model of the quantised hyperbolic automorphisms of the 2-torus is examined in detail.

quant-ph↗
arXiv2003

Quantum Dynamical Entropies in Discrete Classical Chaos

We discuss certain analogies between quantization and discretization of classical systems on manifolds. In particular, we will apply the quantum dynamical entropy of Alicki and Fannes to numerically study the footprints of chaos in discretized versions of hyperbolic maps on the torus.

math-ph↗
arXiv2003

Complete positivity and dissipative factorized dynamics: some comments

After reviewing the main properties of time-evolutions of open quantum systems, some considerations about the positivity of factorized Markovian dynamics for bipartite systems are made. In particular, it is shown that the positivity of the whole time-evolution in general does not ask for the complete positivity of the single system time-evolutions, if they are allowed to differ. However, they must be completely positive if one is a small perturbation of the other, which is the typical situation for open systems in a heat bath.

quant-ph↗
arXiv2003

Neutral kaons in random media

The generalized dynamics describing the propagation of neutral kaons in randomly fluctuating media is derived and analyzed. It takes into account possible matter-induced effects leading to loss of phase coherence and dissipation. The study of selected neutral kaon observables indicates that these non-standard effects are amenable to a direct experimental analysis.

hep-ph↗
arXiv2003

About non-positive evolutions in open system dynamics

The long-time evolution of a system in interaction with an external environment is usually described by a family of linear maps g_t, generated by master equations of Block-Redfield type. These maps are in general non-positive; a widely adopted cure for this physical inconsistency is to restrict the domain of definition of the dynamical maps to those states for which g_t remains positive. We show that this prescription has to be modified when two systems are immersed in the same environment and evolve with the factorized dynamics g_t x g_t starting from an entangled initial state.

quant-ph↗