Decoherence properties of arbitrarily long histories

Within the decoherent histories formulation of quantum mechanics, we consider arbitrarily long histories constructed from a fixed projective partition of a finite-dimensional Hilbert space. We review some of the decoherence properties of such histories including simple necessary decoherence conditions and the dependence of decoherence on the initial state. Here we make a first step towards generalization of our earlier results [Scherer and Soklakov, e-print: quant-ph/0405080, (2004) and Scherer et al., Phys. Lett. A, vol. 326, 307, (2004)] to the case of approximate decoherence.Comment: 8 pages, no figure

Continuous-mode effects and photon-photon phase gate performance

The effects arising from the inherent continuous-mode nature of photonic pulses were poorly understood but significantly influence the performance of quantum devices employing photonic pulse interaction in nonlinear media. Such effects include the entanglement between the continuous wave-vector modes due to pulse interaction as well as the consequence of a finite system bandwidth. We present the first analysis on these effects for interactions between single-photon pulses, demonstrating their impact on the performance of quantum phase gates based on such process. Our study clarifies a realistic picture of this type of quantum devices.Comment: Published Versio

Quantum states prepared by realistic entanglement swapping

Entanglement swapping between photon pairs is a fundamental building block in schemes using quantum relays or quantum repeaters to overcome the range limits of long-distance quantum key distribution. We develop a closed-form solution for the actual quantum states prepared by realistic entanglement swapping, which takes into account experimental deficiencies due to inefficient detectors, detector dark counts, and multiphoton-pair contributions of parametric down-conversion sources. We investigate how the entanglement present in the final state of the remaining modes is affected by the real-world imperfections. To test the predictions of our theory, comparison with previously published experimental entanglement swapping is provided.Comment: 44 pages, 7 figures, Published with minor changes in Phys. Rev.

Initial states and decoherence of histories

We study decoherence properties of arbitrarily long histories constructed from a fixed projective partition of a finite dimensional Hilbert space. We show that decoherence of such histories for all initial states that are naturally induced by the projective partition implies decoherence for arbitrary initial states. In addition we generalize the simple necessary decoherence condition [Scherer et al., Phys. Lett. A (2004)] for such histories to the case of arbitrary coarse-graining.Comment: 10 page

Production of heralded pure single photons from imperfect sources using cross phase modulation

Realistic single-photon sources do not generate single photons with certainty. Instead they produce statistical mixtures of photons in Fock states $\ket{1}$ and vacuum (noise). We describe how to eliminate the noise in the output of the sources by means of another noisy source or a coherent state and cross phase modulation (XPM). We present a scheme which announces the production of pure single photons and thus eliminates the vacuum contribution. This is done by verifying a XPM related phase shift with a Mach-Zehnder interferometer.Comment: 8 pages, 8 EPS figures, RevTeX4. Following changes have been made in v.3: Title and abstract slightly changed; numerous minor revisions and clarifications within the text; an appendix with three new figures has been added. In version v4 we have included a supplementary analysis of our scheme that takes into account absorption losses. Our analysis is heuristic and based on a phenomenological model, which is independent of the physical realization of the proposed scheme. We have estimated upper bounds up to which absorption losses can be tolerated, so as our scheme to improve the efficiency of single photon sources still works. Accepted for publication in Phys. Rev.

Classical predictability and coarse-grained evolution of the quantum baker's map

We investigate how classical predictability of the coarse-grained evolution of the quantum baker's map depends on the character of the coarse-graining. Our analysis extends earlier work by Brun and Hartle [Phys. Rev. D 60, 123503 (1999)] to the case of a chaotic map. To quantify predictability, we compare the rate of entropy increase for a family of coarse-grainings in the decoherent histories formalism. We find that the rate of entropy increase is dominated by the number of scales characterising the coarse-graining.Comment: 28 pages, 1 figur

Non-convex Quadratic Programming Using Coherent Optical Networks

We investigate the possibility of solving continuous non-convex optimization problems using a network of interacting quantum optical oscillators. We propose a native encoding of continuous variables in analog signals associated with the quadrature operators of a set of quantum optical modes. Optical coupling of the modes and noise introduced by vacuum fluctuations from external reservoirs or by weak measurements of the modes are used to optically simulate a diffusion process on a set of continuous random variables. The process is run sufficiently long for it to relax into the steady state of an energy potential defined on a continuous domain. As a first demonstration, we numerically benchmark solving box-constrained quadratic programming (BoxQP) problems using these settings. We consider delay-line and measurement-feedback variants of the experiment. Our benchmarking results demonstrate that in both cases the optical network is capable of solving BoxQP problems over three orders of magnitude faster than a state-of-the-art classical heuristic.Comment: 10 pages, 5 figure