Bell non-locality in two-mode Gaussian states revealed via local squeezing

Local unitary transforms cannot affect the quantum correlations between two systems sharing an entangled state although they do influence the outcomes of local measurements. By considering local squeezing operations we introduce an extended family of observables allowing violation of the CHSH Bell inequality for two-mode Gaussian systems. We show that local squeezing can enable or enhance the identification of non-local two-mode states. In particular, we show that local squeezing followed by photons/no-photons discrimination can suffice to reveal non-locality in a broad ensemble of pure and mixed two-mode Gaussian states

Quantum random walk on the line as a markovian process

We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic increase in the variance of the quantum walker's position with time is a direct consequence of the coherence of the quantum evolution. If the evolution is decoherent, as in the classical case, the variance is shown to increase linearly with time, as expected. Furthermore we show that this system has an evolution operator analogous to that of a resonant quantum kicked rotor. As this rotator may be described through a quantum computational algorithm, one may employ this algorithm to describe the time evolution of the quantum walker.Comment: few typos corrected, 13 pages, 2 figures, to appear in Physica

Decoherence in the quantum walk on the line

We investigate the quantum walk on the line when decoherences are introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. Both mechanisms drive the system to a classical diffusive behavior. In the case of measurements, we show that the diffusion coefficient is proportional to the variance of the initially localized quantum random walker just before the first measurement. When links between neighboring sites are randomly broken with probability $p$ per unit time, the evolution becomes decoherent after a characteristic time that scales as $1/p$. The fact that the quadratic increase of the variance is eventually lost even for very small frequencies of disrupting events, suggests that the implementation of a quantum walk on a real physical system may be severely limited by thermal noise and lattice imperfections.Comment: Elsevier style, 18 pages. New enhanced version with more material: new title, a new section was added and the discussion was updated; references added; submitted to Physica

Generalized Quantum Walk in Momentum Space

We consider a new model of quantum walk on a one-dimensional momentum space that includes both discrete jumps and continuous drift. Its time evolution has two stages; a Markov diffusion followed by localized dynamics. As in the well known quantum kicked rotor, this model can be mapped into a localized one-dimensional Anderson model. For exceptional (rational) values of its scale parameter, the system exhibits resonant behavior and reduce to the usual discrete time quantum walk on the line.Comment: 11 pages, 5 figure