S. Kiesewetter

Pulsed Entanglement of Two Optomechanical Oscillators and Furry’s Hypothesis

A strategy for generating entanglement between two separated optomechanical oscillators is analyzed, using entangled radiation produced from down-conversion and stored in an initiating cavity. We show that the use of pulsed entanglement with optimally shaped temporal modes can efficiently transfer quantum entanglement into a mechanical mode, then remove it after a fixed waiting time for measurement. This protocol could provide new avenues for testing for bounds on decoherence in massive systems that are spatially separated, as originally suggested by Furry not long after the discussion by Einstein-Podolsky-Rosen and Schrödinger of entanglement.

Decoherence of Einstein–Podolsky–Rosen steering

We consider two systems A and B that share Einstein–Podolsky–Rosen (EPR) steering correlations and study how these correlations will decay when each of the systems is independently coupled to a reservoir. EPR steering is a directional form of entanglement, and the measure of steering can change depending on whether system A is steered by B, or vice versa. First, we examine the decay of the steering correlations of the two-mode squeezed state. We find that if system B is coupled to a reservoir, then the decoherence of the steering of A by B is particularly marked, to the extent that there is a sudden death of steering after a finite time. We find a different directional effect if the reservoirs are thermally excited. Second, we study the decoherence of the steering of a Schrodinger cat state, modeled as the entangled state of a spin and harmonic oscillator, when the macroscopic system (the cat) is coupled to a reservoir.

Algorithms for integration of stochastic differential equations using parallel optimized sampling in the Stratonovich calculus

Abstract A variance reduction method for stochastic integration of Fokker–Planck equations is derived. This unifies the cumulant hierarchy and stochastic equation approaches to obtaining moments, giving a performance superior to either. We show that the brute force method of reducing sampling error by just using more trajectories in a sampled stochastic equation is not the best approach. The alternative of using a hierarchy of moment equations is also not optimal, as it may converge to erroneous answers. Instead, through Bayesian conditioning of the stochastic noise on the requirement that moment equations are satisfied, we obtain improved results with reduced sampling errors for a given number of stochastic trajectories. The method used here converges faster in time-step than Ito–Euler algorithms. This parallel optimized sampling (POS) algorithm is illustrated by several examples, including a bistable nonlinear oscillator case where moment hierarchies fail to converge.

Parallel Optimized Sampling for Stochastic Equations

Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales proportionate to

Einstein–Podolsky–Rosen quantum simulations in nonclassical phase-space

1/N_{S}

Scalable quantum simulation of pulsed entanglement and Einstein-Podolsky-Rosen steering in optomechanics

for

Simulation of an optomechanical quantum memory in the nonlinear regime

N_{S}

Creation, storage and retrieval of an optomechanical cat.

samples. In this paper, we obtain a new class of variance reduction methods for treating stochastic equations, called parallel optimized sampling. The objective of parallel optimized sampling is to reduce the sampling variance in the observables of an ensemble of stochastic trajectories. This is achieved through calculating a finite set of observables---typically statistical moments---in parallel and minimizing the errors compared to known values. The algorithm is both numerically efficient and unbiased. Importantly, it does not increase the errors in higher-order moments and generally reduces such errors as well. The same procedure is applied both to initial ensembles and to changes in a finite time-step. Results of these methods sh...

First-principles simulation of an optomechanical memory for quantum entanglement

We give a brief history of probabilistic quantum simulations of Einstein–Podolsky–Rosen paradoxes. This treats the early origins of the modern proposals using continuous variables, simulation methods using the positive-P representation, and current developments. Recent simulations treated include the behavior of parametric downconversion near the critical point, the simulation of parametric Bell violations, quantum entanglement, and correlations in optomechanics, as well as extensions to quantum field systems with planar interferometers.