543 research outputs found
A system-theoretic framework for privacy preservation in continuous-time multiagent dynamics
In multiagent dynamical systems, privacy protection corresponds to avoid
disclosing the initial states of the agents while accomplishing a distributed
task. The system-theoretic framework described in this paper for this scope,
denoted dynamical privacy, relies on introducing output maps which act as
masks, rendering the internal states of an agent indiscernible by the other
agents as well as by external agents monitoring all communications. Our output
masks are local (i.e., decided independently by each agent), time-varying
functions asymptotically converging to the true states. The resulting masked
system is also time-varying, and has the original unmasked system as its limit
system. When the unmasked system has a globally exponentially stable
equilibrium point, it is shown in the paper that the masked system has the same
point as a global attractor. It is also shown that existence of equilibrium
points in the masked system is not compatible with dynamical privacy.
Application of dynamical privacy to popular examples of multiagent dynamics,
such as models of social opinions, average consensus and synchronization, is
investigated in detail.Comment: 38 pages, 4 figures, extended version of arXiv preprint
arXiv:1808.0808
On the generation of sequential unitary gates from continuous time Schrodinger equations driven by external fields
In all the various proposals for quantum computers, a common feature is that
the quantum circuits are expected to be made of cascades of unitary
transformations acting on the quantum states. A framework is proposed to
express these elementary quantum gates directly in terms of the control inputs
entering into the continuous time forced Schrodinger equation.Comment: 10 page
Representing multiqubit unitary evolutions: spin coherences and infinitesimal coherences
For the tensor of coherences parametrization of a multiqubit density
operator, we provide an explicit formulation of the corresponding unitary
dynamics at infinitesimal level. The main advantage of this formalism (clearly
reminiscent of the idea of ``coherences'' and ``coupling Hamiltonians'' of spin
systems) is that the pattern of correlation between qubits and the pattern of
infinitesimal correlation are highlighted simultaneously and can be used
constructively for qubit manipulation. For example, it allows to compute
explicitly a Rodrigues' formula for the one-parameter orbits of nonlocal
Hamiltonians. The result is easily generalizable to orbits of Cartan
subalgebras and allows to write the Cartan decomposition of unitary propagators
as a linear action.Comment: significantly rewritten, 9 pages, 4 figure
The geometric phase of stock trading
Geometric phases describe how in a continuous-time dynamical system the
displacement of a variable (called phase variable) can be related to other
variables (shape variables) undergoing a cyclic motion, according to an area
rule. The aim of this paper is to show that geometric phases can exist also for
discrete-time systems, and even when the cycles in shape space have zero area.
A context in which this principle can be applied is stock trading. A zero-area
cycle in shape space represents the type of trading operations normally carried
out by high-frequency traders (entering and exiting a position on a fast
time-scale), while the phase variable represents the cash balance of a trader.
Under the assumption that trading impacts stock prices, even zero-area cyclic
trading operations can induce geometric phases, i.e., profits or losses,
without affecting the stock quote.Comment: 15 pages, 12 figure
Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control
In this paper we investigate parametrization-free solutions of the problem of
quantum pure state preparation and subspace stabilization by means of
Hamiltonian control, continuous measurement and quantum feedback, in the
presence of a Markovian environment. In particular, we show that whenever
suitable dissipative effects are induced either by the unmonitored environment
or by non Hermitian measurements, there is no need for feedback control to
accomplish the task. Constructive necessary and sufficient conditions on the
form of the open-loop controller can be provided in this case. When open-loop
control is not sufficient, filtering-based feedback control laws steering the
evolution towards a target pure state are provided, which generalize those
available in the literature
Controllability properties for finite dimensional quantum Markovian master equations
Various notions from geometric control theory are used to characterize the
behavior of the Markovian master equation for N-level quantum mechanical
systems driven by unitary control and to describe the structure of the sets of
reachable states. It is shown that the system can be accessible but neither
small-time controllable nor controllable in finite time. In particular, if the
generators of quantum dynamical semigroups are unital, then the reachable sets
admit easy characterizations as they monotonically grow in time. The two level
case is treated in detail.Comment: 15 page
Controllability of Quantum Systems
An overview and synthesis of results and criteria for open-loop
controllability of Hamiltonian quantum systems obtained using Lie group and Lie
algebra techniques is presented. Negative results for open-loop controllability
of dissipative systems are discussed, and the superiority of closed-loop
(feedback) control for quantum systems is established.Comment: 6 pages, to appear in Proceedings of Conference on Lagrangian and
Hamiltonian Methods in Non-Linear Control (Seville, Spain, 2003
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