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

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

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

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

Quantum resources for purification and cooling: fundamental limits and opportunities

Preparing a quantum system in a pure state is ultimately limited by the nature of the system's evolution in the presence of its environment and by the initial state of the environment itself. We show that, when the system and environment are initially uncorrelated and arbitrary joint unitary dynamics is allowed, the system may be purified up to a certain (possibly arbitrarily small) threshold if and only if its environment, either natural or engineered, contains a "virtual subsystem" which has the same dimension and is in a state with the desired purity. Beside providing a unified understanding of quantum purification dynamics in terms of a "generalized swap process," our results shed light on the significance of a no-go theorem for exact ground-state cooling, as well as on the quantum resources needed for achieving an intended purification task.Comment: 10 pages, 2 figure