6,842 research outputs found
Continuous-variable entanglement distillation and non-commutative central limit theorems
Entanglement distillation transforms weakly entangled noisy states into
highly entangled states, a primitive to be used in quantum repeater schemes and
other protocols designed for quantum communication and key distribution. In
this work, we present a comprehensive framework for continuous-variable
entanglement distillation schemes that convert noisy non-Gaussian states into
Gaussian ones in many iterations of the protocol. Instances of these protocols
include (a) the recursive-Gaussifier protocol, (b) the temporally-reordered
recursive-Gaussifier protocol, and (c) the pumping-Gaussifier protocol. The
flexibility of these protocols give rise to several beneficial trade-offs
related to success probabilities or memory requirements, which that can be
adjusted to reflect experimental demands. Despite these protocols involving
measurements, we relate the convergence in this protocols to new instances of
non-commutative central limit theorems, in a formalism that we lay out in great
detail. Implications of the findings for quantum repeater schemes are
discussed.Comment: published versio
Nonlinear oscillator with parametric colored noise: some analytical results
The asymptotic behavior of a nonlinear oscillator subject to a multiplicative
Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in
terms of energy-angle coordinates, it is observed that the angle is a fast
variable as compared to the energy. Thus, an effective stochastic dynamics for
the energy can be derived if the angular variable is averaged out. However, the
standard elimination procedure, performed earlier for a Gaussian white noise,
fails when the noise is colored because of correlations between the noise and
the fast angular variable. We develop here a specific averaging scheme that
retains these correlations. This allows us to calculate the probability
distribution function (P.D.F.) of the system and to derive the behavior of
physical observables in the long time limit
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