Quantum Trajectories for Realistic Detection

Quantum trajectories describe the stochastic evolution of an open quantum system conditioned on continuous monitoring of its output, such as by an ideal photodetector. Here we derive (non-Markovian) quantum trajectories for realistic photodetection, including the effects of efficiency, dead time, bandwidth, electronic noise, and dark counts. We apply our theory to a realistic cavity QED scenario and investigate the impact of such detector imperfections on the conditional evolution of the system state. A practical theory of quantum trajectories with realistic detection will be essential for experimental and technological applications of quantum feedback in many areas.Comment: 5 pages, 4 figures (3 .eps included, 1 jpeg as an additional file). To be published in Phys. Rev.

Autonomous thermal machine for amplification and control of energetic coherence

We present a model for an autonomous quantum thermal machine comprised of two qubits capable of manipulating and even amplifying the local coherence in a non-degenerate external system. The machine uses only thermal resources, namely, contact with two heat baths at different temperatures, and the external system has a non-zero initial amount of coherence. The method we propose allows for an interconversion between energy, both work and heat, and coherence in an autonomous configuration working in out-of-equilibrium conditions. This model raises interesting questions about the role of fundamental limitations on transformations involving coherence and opens up new possibilities in the manipulation of coherence by autonomous thermal machines.Comment: v1: 5 + 3 pages, 2 figures. v2: Restructured version with several new results and a new appendix, 11 + 14 pages, 4 + 3 figures. v3: Improved and corrected version with new discussions, 8 + 8 pages, 4 + 3 figure

Jump-like unravelings for non-Markovian open quantum systems

Non-Markovian evolution of an open quantum system can be `unraveled' into pure state trajectories generated by a non-Markovian stochastic (diffusive) Schr\"odinger equation, as introduced by Di\'osi, Gisin, and Strunz. Recently we have shown that such equations can be derived using the modal (hidden variable) interpretation of quantum mechanics. In this paper we generalize this theory to treat jump-like unravelings. To illustrate the jump-like behavior we consider a simple system: A classically driven (at Rabi frequency $\Omega$) two-level atom coupled linearly to a three mode optical bath, with a central frequency equal to the frequency of the atom, $\omega_0$, and the two side bands have frequencies $\omega_0\pm\Omega$. In the large $\Omega$ limit we observed that the jump-like behavior is similar to that observed in this system with a Markovian (broad band) bath. This is expected as in the Markovian limit the fluorescence spectrum for a strongly driven two level atom takes the form of a Mollow triplet. However the length of time for which the Markovian-like behaviour persists depends upon {\em which} jump-like unraveling is used.Comment: 11 pages, 5 figure

A perturbative approach to non-Markovian stochastic Schr\"odinger equations

In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian Stochastic Schr\"odinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two level atom immersed in a environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensembled average state $\rho_{\rm red}(t)$ approach the exact reduced state found via Imamo\=glu's enlarged system method [Phys. Rev. A. 50, 3650 (1994)].Comment: 17 pages, 4 figure

Hiding variables when decomposing specifications into GR(1) contracts

We propose a method for eliminating variables from component specifications during the decomposition of GR(1) properties into contracts. The variables that can be eliminated are identified by parameterizing the communication architecture to investigate the dependence of realizability on the availability of information. We prove that the selected variables can be hidden from other components, while still expressing the resulting specification as a game with full information with respect to the remaining variables. The values of other variables need not be known all the time, so we hide them for part of the time, thus reducing the amount of information that needs to be communicated between components. We improve on our previous results on algorithmic decomposition of GR(1) properties, and prove existence of decompositions in the full information case. We use semantic methods of computation based on binary decision diagrams. To recover the constructed specifications so that humans can read them, we implement exact symbolic minimal covering over the lattice of integer orthotopes, thus deriving minimal formulae in disjunctive normal form over integer variable intervals

Verifying Safety Properties With the TLA+ Proof System

TLAPS, the TLA+ proof system, is a platform for the development and mechanical verification of TLA+ proofs written in a declarative style requiring little background beyond elementary mathematics. The language supports hierarchical and non-linear proof construction and verification, and it is independent of any verification tool or strategy. A Proof Manager uses backend verifiers such as theorem provers, proof assistants, SMT solvers, and decision procedures to check TLA+ proofs. This paper documents the first public release of TLAPS, distributed with a BSD-like license. It handles almost all the non-temporal part of TLA+ as well as the temporal reasoning needed to prove standard safety properties, in particular invariance and step simulation, but not liveness properties

Coherent information analysis of quantum channels in simple quantum systems

The coherent information concept is used to analyze a variety of simple quantum systems. Coherent information was calculated for the information decay in a two-level atom in the presence of an external resonant field, for the information exchange between two coupled two-level atoms, and for the information transfer from a two-level atom to another atom and to a photon field. The coherent information is shown to be equal to zero for all full-measurement procedures, but it completely retains its original value for quantum duplication. Transmission of information from one open subsystem to another one in the entire closed system is analyzed to learn quantum information about the forbidden atomic transition via a dipole active transition of the same atom. It is argued that coherent information can be used effectively to quantify the information channels in physical systems where quantum coherence plays an important role.Comment: 24 pages, 7 figs; Final versiob after minor changes, title changed; to be published in Phys. Rev. A, September 200

Straightforward synthesis of functionalized cyclic polymers in high yield via RAFT and thiolactone-disulfide chemistry

An efficient synthetic pathway toward cyclic polymers based on the combination of thiolactone and disulfide chemistry has been developed. First, heterotelechelic linear polystyrene (PS) containing an alpha-thiolactone (TLa) and an omega-dithiobenzoate group was synthesized via reversible addition-fragmentation chain transfer (RAFT) polymerization, employing a newly designed TLa-bearing chain transfer agent (CTA). The subsequent reaction of this heterotelechelic polymer with an amine, which acts as a nucleophile for both the TLa and dithiobenzoate units, generated the alpha,omega-thiol-telechelic PS under ambient conditions without the need for any catalyst or other additives. The arrangement of thiols under a high dilution afforded single cyclic PS (c-PS) through an oxidative disulfide linkage. The cyclic PS (c-PS) disulfide ring formation was evidenced by SEC, MALDI-TOF MS and H-1-NMR characterization. Moreover, we demonstrated a controlled ring opening via either disulfide reduction or thiol-disulfide exchange to enable easy and clean topology transformation. Furthermore, to illustrate the broad utility of this synthetic methodology, different amines including functional ones were employed, allowing for the one-step preparation of functionalized cyclic polymers with high yields

TLA+ Proofs

TLA+ is a specification language based on standard set theory and temporal logic that has constructs for hierarchical proofs. We describe how to write TLA+ proofs and check them with TLAPS, the TLA+ Proof System. We use Peterson's mutual exclusion algorithm as a simple example to describe the features of TLAPS and show how it and the Toolbox (an IDE for TLA+) help users to manage large, complex proofs.Comment: A shorter version of this article appeared in the proceedings of the conference Formal Methods 2012 (FM 2012, Paris, France, Springer LNCS 7436, pp. 147-154