911 research outputs found
Probabilistic Quantum Control Via Indirect Measurement
The most basic scenario of quantum control involves the organized
manipulation of pure dynamical states of the system by means of unitary
transformations. Recently, Vilela Mendes and Mank'o have shown that the
conditions for controllability on the state space become less restrictive if
unitary control operations may be supplemented by projective measurement. The
present work builds on this idea, introducing the additional element of
indirect measurement to achieve a kind of remote control. The target system
that is to be remotely controlled is first entangled with another identical
system, called the control system. The control system is then subjected to
unitary transformations plus projective measurement. As anticipated by
Schrodinger, such control via entanglement is necessarily probabilistic in
nature. On the other hand, under appropriate conditions the remote-control
scenario offers the special advantages of robustness against decoherence and a
greater repertoire of unitary transformations. Simulations carried out for a
two-level system demonstrate that, with optimization of control parameters, a
substantial gain in the population of reachable states can be realized.Comment: 9 pages, 2 figures; typos added, reference added, reference remove
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 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
Coherent Quantum Filtering for Physically Realizable Linear Quantum Plants
The paper is concerned with a problem of coherent (measurement-free)
filtering for physically realizable (PR) linear quantum plants. The state
variables of such systems satisfy canonical commutation relations and are
governed by linear quantum stochastic differential equations, dynamically
equivalent to those of an open quantum harmonic oscillator. The problem is to
design another PR quantum system, connected unilaterally to the output of the
plant and playing the role of a quantum filter, so as to minimize a mean square
discrepancy between the dynamic variables of the plant and the output of the
filter. This coherent quantum filtering (CQF) formulation is a simplified
feedback-free version of the coherent quantum LQG control problem which remains
open despite recent studies. The CQF problem is transformed into a constrained
covariance control problem which is treated by using the Frechet
differentiation of an appropriate Lagrange function with respect to the
matrices of the filter.Comment: 14 pages, 1 figure, submitted to ECC 201
- …