714 research outputs found
Symmetrizing quantum dynamics beyond gossip-type algorithms
Recently, consensus-type problems have been formulated in the quantum domain.
Obtaining average quantum consensus consists in the dynamical symmetrization of
a multipartite quantum system while preserving the expectation of a given
global observable. In this paper, two improved ways of obtaining consensus via
dissipative engineering are introduced, which employ on quasi local preparation
of mixtures of symmetric pure states, and show better performance in terms of
purity dynamics with respect to existing algorithms. In addition, the first
method can be used in combination with simple control resources in order to
engineer pure Dicke states, while the second method guarantees a stronger type
of consensus, namely single-measurement consensus. This implies that outcomes
of local measurements on different subsystems are perfectly correlated when
consensus is achieved. Both dynamics can be randomized and are suitable for
feedback implementation.Comment: 11 pages, 3 figure
On entropy production for controlled Markovian evolution
We consider thermodynamic systems with finitely many degrees of freedom and
subject to an external control action. We derive some basic results on the
dependence of the relative entropy production rate on the controlling force.
Applications to macromolecular cooling and to controlling the convergence to
equilibrium rate are sketched. Analogous results are derived for closed and
open n-level quantum systems.Comment: 19 page
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
Decompositions of Hilbert Spaces, Stability Analysis and Convergence Probabilities for Discrete-Time Quantum Dynamical Semigroups
We investigate convergence properties of discrete-time semigroup quantum
dynamics, including asymptotic stability, probability and speed of convergence
to pure states and subspaces. These properties are of interest in both the
analysis of uncontrolled evolutions and the engineering of controlled dynamics
for quantum information processing. Our results include two Hilbert space
decompositions that allow for deciding the stability of the subspace of
interest and for estimating of the speed of convergence, as well as a formula
to obtain the limit probability distribution for a set of orthogonal invariant
subspaces.Comment: 14 pages, no figures, to appear in Journal of Physics A, 201
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
Switching Quantum Dynamics for Fast Stabilization
Control strategies for dissipative preparation of target quantum states, both
pure and mixed, and subspaces are obtained by switching between a set of
available semigroup generators. We show that the class of problems of interest
can be recast, from a control--theoretic perspective, into a
switched-stabilization problem for linear dynamics. This is attained by a
suitable affine transformation of the coherence-vector representation. In
particular, we propose and compare stabilizing time-based and state-based
switching rules for entangled state preparation, showing that the latter not
only ensure faster convergence with respect to non-switching methods, but can
designed so that they retain robustness with respect to initialization, as long
as the target is a pure state or a subspace.Comment: 15 pages, 4 figure
Engineering Stable Discrete-Time Quantum Dynamics via a Canonical QR Decomposition
We analyze the asymptotic behavior of discrete-time, Markovian quantum
systems with respect to a subspace of interest. Global asymptotic stability of
subspaces is relevant to quantum information processing, in particular for
initializing the system in pure states or subspace codes. We provide a
linear-algebraic characterization of the dynamical properties leading to
invariance and attractivity of a given quantum subspace. We then construct a
design algorithm for discrete-time feedback control that allows to stabilize a
target subspace, proving that if the control problem is feasible, then the
algorithm returns an effective control choice. In order to prove this result, a
canonical QR matrix decomposition is derived, and also used to establish the
control scheme potential for the simulation of open-system dynamics.Comment: 12 pages, 1 figur
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
Discrete-Time Controllability for Feedback Quantum Dynamics
Controllability properties for discrete-time, Markovian quantum dynamics are
investigated. We find that, while in general the controlled system is not
finite-time controllable, feedback control allows for arbitrary asymptotic
state-to-state transitions. Under further assumption on the form of the
measurement, we show that finite-time controllability can be achieved in a time
that scales linearly with the dimension of the system, and we provide an
iterative procedure to design the unitary control actions
- …