Randomized control of open quantum systems

The problem of open-loop dynamical control of generic open quantum systems is addressed. In particular, I focus on the task of effectively switching off environmental couplings responsible for unwanted decoherence and dissipation effects. After revisiting the standard framework for dynamical decoupling via deterministic controls, I describe a different approach whereby the controller intentionally acquires a random component. An explicit error bound on worst-case performance of stochastic decoupling is presented.Comment: 6 pages, no figure, requires IEEEtran LaTe

Aid for Trade: Supporting the Use of Standards

As a complementary activity to the WTO’s Doha Round of trade negotiations, the Sixth Ministerial Conference in Hong Kong, China, in 2005 mandated that technical assistance and capacity-building activities needed to be expanded so that developing countries could take better advantage of the opportunities opened up by trade liberalization.With traditional barriers to trade such as tariffs and quotas being progressively eliminated, the ability to comply with technical regulations and use international standards has emerged as a key factor for success in integrating into international markets. This paper focuses on the potential of providing assistance to Governments and businesses for the setting of and complying with product standards as part of the AId for Trade initiative.Aid for Trade, transition economies, product standards

Quantum and classical resources for unitary design of open-system evolutions

A variety of tasks in quantum control, ranging from purification and cooling to quantum stabilisation and open-system simulation, rely on the ability to implement a target quantum channel over a specified time interval within prescribed accuracy. This can be achieved by engineering a suitable unitary dynamics of the system of interest along with its environment, which, depending on the available level of control, is fully or partly exploited as a coherent quantum controller. After formalising a controllability framework for completely positive trace-preserving quantum dynamics, we provide sufficient conditions on the environment state and dimension that allow for the realisation of relevant classes of quantum channels, including extreme channels, stochastic unitaries or simply any channel. The results hinge on generalisations of Stinespring's dilation via a subsystem principle. In the process, we show that a conjecture by Lloyd on the minimal dimension of the environment required for arbitrary open-system simulation, albeit formally disproved, can in fact be salvaged, provided that classical randomisation is included among the available resources. Existing measurement-based feedback protocols for universal simulation, dynamical decoupling and dissipative state preparation are recast within the proposed coherent framework as concrete applications, and the resources they employ discussed in the light of the general results

Lindblad Approach to Nonlinear Jaynes-Cummings Dynamics of a Trapped Ion

The Lindblad approach to open quantum systems is introduced for studying the dynamics of a single trapped ion prepared in nonclassical motional states and subjected to continuous measurement of its internal population. This results in an inhibition of the dynamics similar to the one occurring in the quantum Zeno effect. In particular, modifications to the Jaynes-Cummings collapses and revivals arising from an initial coherent state of motion in various regimes of interaction with the driving laser are dealt in detail.Comment: 5 Pages, 3 figures available upon request; Plain REVTeX; to be published in Physical Review

Thresholds for macroparasite infections

We analyse here the equilibria of an infinite system of partial differential equations modelling the dynamics of a population infected by macroparasites. We find that it is possible to define a reproduction number R0 that satisfies the intuitive definition, and yields a sharp threshold in the behaviour of the system: when R0 1, the PFE is unstable and there exists a unique endemic equilibrium. The results mainly confirm what had been obtained in simplified models, except for the fact that no backwards bifurcation occur in this model. The stability of equilibria is established by extending an abstract linearization principle and by analysing the spectra of appropriate operators

Quantum Markovian Subsystems: Invariance, Attractivity, and Control

We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing, subsystem encodings offering a general pathway to faithfully represent quantum information. We provide explicit linear-algebraic characterizations of the notion of invariant and noiseless subsystem for Markovian master equations, under different robustness assumptions for model-parameter and initial-state variations. The stronger concept of an attractive quantum subsystem is introduced, and sufficient existence conditions are identified based on Lyapunov's stability techniques. As a main control application, we address the potential of output-feedback Markovian control strategies for quantum pure state-stabilization and noiseless-subspace generation. In particular, explicit results for the synthesis of stabilizing semigroups and noiseless subspaces in finite-dimensional Markovian systems are obtained.Comment: 16 pages, no figures. Revised version with new title, corrected typos, partial rewriting of Section III.E and some other minor change