Classical dilations \`a la Hudson-Parthasarathy of Markov semigroups

We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup defined in Quantum Probability via quantum stochastic differential equations. Given a homogeneous Markov chain in continuous time in a finite state space E, we introduce a second system, an environment, and a deterministic invertible time-homogeneous global evolution of the system E with this environment such that the original Markov evolution of E can be realized by a proper choice of the initial random state of the environment. We also compare this dilations with the dilations of a quantum dynamical semigroup in Quantum Probability: given a classical Markov semigroup, we extend it to a proper quantum dynamical semigroup for which we can find a Hudson-Parthasarathy dilation which is itself an extension of our classical dilation

On quantum error-correction by classical feedback in discrete time

We consider the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment. For discrete time Markovian evolutions, in the case of fixed measurement on the environment, we give criteria for quantum information to be perfectly corrigible and characterize the related feedback. Then we analyze the case when perfect correction is not possible and, in the qubit case, we find optimal feedback maximizing the channel fidelity.Comment: 11 pages, 1 figure, revtex

Bell's Inequality Violations: Relation with de Finetti's Coherence Principle and Inferential Analysis of Experimental Data

It is often believed that de Finetti's coherence principle naturally leads, in the nite case, to the Kolmogorov's probability theory of random phenomena, which then implies Bell's inequality. Thus, not only a violation of Bell's inequality looks paradoxical in the Kolmogorovian framework, but it should violate also de Finetti's coherence principle. Firstly, we show that this is not the case: the typical theoretical violations of Bell's inequality in quantum physics are in agreement with de Finetti's coherence principle. Secondly, we look for statistical evidence of such violations: we consider the experimental data of measurements of polarization of photons, performed to verify empirically violations of Bell's inequality, and, on the basis of the estimated violation, we test the null hypothesis of Kolmogorovianity for the observed phenomenon. By standard inferential techniques we compute the p-value for the test and get a clear strong conclusion against the Kolmogorovian hypothesis

Optimal entanglement manipulation via coherent-state transmission

We derive an optimal bound for arbitrary entanglement manipulation based on the transmission of a pulse in coherent states over a lossy channel followed by local operations and unlimited classical communication (LOCC). This stands on a theorem to reduce LOCC via a local unital qubit channel to local filtering. We also present an optimal protocol based on beam splitters and a quantum nondemolition (QND) measurement on photons. Even if we replace the QND measurement with photon detectors, the protocol outperforms known entanglement generation schemes.Comment: 5 pages, 1 figur

Quantum trajectories, feedback and squeezing

Quantum trajectory theory is the best mathematical set up to model continual observations of a quantum system and feedback based on the observed output. Inside this framework, we study how to enhance the squeezing of the fluorescence light emitted by a two-level atom, stimulated by a coherent monochromatic laser. In the presence of a Wiseman-Milburn feedback scheme, based on the homodyne detection of a fraction of the emitted light, we analyze the squeezing dependence on the various control parameters.Comment: 8 pages, 2 figures, "Noise Information & Complexity @ Quantum Scale" Proceeding

Spin chains and channels with memory

In most studies of the channel capacity of quantum channels, it is assumed that the errors in each use of the channel are independent. However, recent work has begun to investigate the effects of memory or correlations in the error. This work has led to speculation that interesting non-analytic behaviour may occur in the capacity. Motivated by these observations, we connect the study of channel capacities under correlated error to the study of critical behaviour in many-body physics. This connection enables us the techniques of many-body physics to either completely solve or understand qualitatively a number of interesting models of correlated error. The models can display analogous behaviour to associated many-body systems, including `phase transitions'.Comment: V2: changes in presentation, some additional comments on generalisation. V3: In accordance with published version, most (but not all) details of proofs now included. A separate paper will shortly be submitted separately with all details and more result

Experimental reversion of the optimal quantum cloning and flipping processes

The quantum cloner machine maps an unknown arbitrary input qubit into two optimal clones and one optimal flipped qubit. By combining linear and non-linear optical methods we experimentally implement a scheme that, after the cloning transformation, restores the original input qubit in one of the output channels, by using local measurements, classical communication and feedforward. This significant teleportation-like method demonstrates how the information is preserved during the cloning process. The realization of the reversion process is expected to find useful applications in the field of modern multi-partite quantum cryptography.Comment: 10 pages, 3 figure