steady states of max łukasiewicz fuzzy systems abstract the paper gives a systematic characterization of the eigenspaces in a max t algebra where t is the ukasiewicz t norm a max ukasiewicz fuzzy algebra can be used for the description of the states of discrete event systems the states can represent a balance between the resources expended during the run of a system for example fuel or money the classification of max ukasiewicz eigenspaces is described and illustrated by two and three dimensional examples in this case it is possible to accompany the example with graphs however the description of the eigenspaces for higher dimensions is also outlined

feedback control of quantum entanglement in a two spin system a pair of spins is the most simple quantum system that can exhibit entanglement a nonclassical property that plays an essential role in quantum information technologies in this paper feedback control problems of a symmetric two spin system conditioned on a continuous measurement are investigated in order to make some useful formulas in stochastic control theory directly applicable we first derive a two dimensional representation of the system we then prove that a feedback controller stabilizes an entangled state of the two spins almost globally with probability one furthermore it is demonstrated that some entangled states which correspond to nonequilibrium points of the dynamics are globally stabilized via feedback in the sense that the mean distance from a target can be reduced to an arbitrarily small value

reachable set of operators on controlled open quantum systems in a markovian environment abstract in this article we propose a framework studying all possible operations one can generate at any given time on quantum systems in a markovian environment a complete characterization of the operations one can simulate at any given time on a qubit in a unital markovian environment is given and possible extensions on general cases are discussed

hamiltonian control of quantum dynamical semigroups stabilization and convergence speed we consider finite dimensional markovian open quantum systems and characterize the extent to which time independent hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed for a generic lindblad master equation we introduce a dissipation induced decomposition of the associated hilbert space and show how it serves both as a tool to analyze global stability properties for given control resources and as the starting point to synthesize controls that ensure rapid convergence the resulting design principles are illustrated in realistic markovian control settings motivated by quantum information processing including quantum optical systems and nitrogen vacancy centers in diamond

brief paper 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 assumptions on the form of the measurement we show that finite time controllability can be achieved in a time that is twice the dimension of the system and we provide an iterative procedure to design the unitary control actions

controllability aspects of quantum dynamics a unified approach for closed and open systems knowledge about to what extent quantum dynamical systems can be steered by coherent controls is indispensable for future developments in quantum technology the purpose of this paper is to analyze such controllability aspects for finite dimensional bilinear quantum control systems we use a unified approach based on lie algebraic methods from nonlinear control theory to revisit known and to establish new results for closed and open quantum systems in particular we provide a simplified characterization of different notions of controllability for closed quantum systems described by the liouville von neumann equation we derive new necessary and sufficient conditions for accessibility of open quantum systems modelled by the lindblad kossakowski master equation to this end we exploit a well studied topic of differential geometry namely the classification of all matrix lie groups which act transitively on the grassmann manifold or the punctured euclidean space for the special case of coupled spin 1 2 systems we obtain a remarkably simple characterization of accessibility these accessibility results correct and refine previous statements in the quantum control literature

geometric optimal control of the contrast imaging problem in nuclear magnetic resonance the objective of this article is to introduce the tools to analyze the contrast imaging problem in nuclear magnetic resonance optimal trajectories can be selected among extremal solutions of the pontryagin maximum principle applied to this mayer type optimal problem such trajectories are associated to the question of extremizing the transfer time hence the optimal problem is reduced to the analysis of the hamiltonian dynamics related to singular extremals and their optimality status this is illustrated by using the examples of cerebrospinal fluid water and grey white matter of cerebrum

controllability of quantum systems with switching control this article focuses on wavefunction controllability of a class of quantum systems with switching control first we present a specific quantum system which is not wavefunction controllable under the action of any one of two controllers with different fixed structures however we prove that the system is wavefunction controllable if the control input is allowed to switch between the two controllers then we present a sufficient condition for wavefunction controllability of a class of quantum systems with switching control and briefly discuss the problem of control design for such quantum control systems finally two illustrative examples are presented to demonstrate a possible control design process for the proposed method

controllability properties of affine systems this paper deals with transitivity controllability of affine families of vector fields on a finite dimensional vector space v in particular we focus on affine families whose corresponding families of linear fields are transitive on v 0 and which in addition have no fixed points in v we show that such families are necessarily transitive on v and we also show that they remain transitive under small perturbations in general however affine families need not remain transitive under small perturbations for example small affine perturbations of transitive linear systems are not necessarily transitive since any affine system mathcal f naturally defines a system mathcal f r of right invariant vector fields on the semi direct product of v with gl v we also investigate transitivity properties mathcal f r our result is that if mathcal f is an affine family satisfying the preceding conditions then mathcal f r generates the full lie algebra on the semi direct product

time minimal control of dissipative two level quantum systems the generic case the objective of this article is to complete preliminary results from the work of bonnard and sugny 2009 and sugny et al 2007 concerning the time minimal control of dissipative two level quantum systems whose dynamics is governed by the lindblad equation the extremal system is described by a 3d hamiltonian depending upon three parameters we combine geometric techniques with numerical simulations to deduce the optimal solutions

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

analysis and synthesis of attractive quantum markovian dynamics we propose a general framework for investigating a large class of stabilization problems in markovian quantum systems building on the notions of invariant and attractive quantum subsystem we characterize attractive subspaces by exploring the structure of the invariant sets for the dynamics our general analysis results are exploited to assess the ability of open loop hamiltonian and output feedback control strategies to synthesize markovian generators which stabilize a target subsystem subspace or pure state in particular we provide an algebraic characterization of the manifold of stabilizable pure states in arbitrary finite dimensional markovian systems that leads to a constructive strategy for designing the relevant controllers implications for stabilization of entangled pure states are addressed by example

modeling and control of quantum systems an introduction the scope of this work is to provide a self contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems as well as a brief survey on the main approaches to control synthesis while part of the existing theory especially in the open loop setting stems directly from classical control theory most notably geometric control and optimal control a number of tools specifically tailored for quantum systems have been developed since the 1980s in order to take into account their distinctive features the probabilistic nature of atomic scale physical systems the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback design problems the relevant dynamical models for both closed and open quantum systems are presented along with the main results on their controllability and stability a brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies

illustrating the geometry of coherently controlled unital open quantum systems we extend standard markovian open quantum systems quantum channels by allowing for hamiltonian controls and elucidate their geometry in terms of lie semigroups for standard dissipative interactions with the environment and different coherent controls we particularly specify the tangent cones lie wedges of the respective lie semigroups of quantum channels these cones are the counterpart of the infinitesimal generator of a single one parameter semigroup they comprise all directions the underlying open quantum system can be steered to and thus give insight into the geometry of controlled open quantum dynamics such a differential characterization is highly valuable for approximating reachable sets of given initial quantum states in a plethora of experimental implementations

control landscapes for open system quantum operations the reliable realization of control operations is a key component of quantum information applications in practice meeting this goal is very demanding for open quantum systems this paper investigates the landscape defined as the fidelity j between the desired and achieved quantum operations with an open system the goal is to maximize j as a functional of the control variables we specify the complete set of critical points of the landscape function in the so called kinematic picture an associated hessian analysis of the landscape reveals that upon the satisfaction of a particular controllability criterion the critical topology is dependent on the particular environment but no false traps i e suboptimal solutions exist thus a gradient type search algorithm should not be hindered in searching for the ultimate optimal solution with such controllable systems moreover the maximal fidelity is proven to coincide with uhlmann s fidelity between the environmental initial states associated with the achieved and desired quantum operations which provides a generalization of uhlmann s theorem in terms of kraus maps

is measurement based feedback still better for quantum control systems in this paper we put forward a fundamental question concerning feedback control of quantum systems is measurement based feedback control still better than open loop control in contrast to the classical control theory the answer is far from obvious this is because measurement based feedback needs measurement to reduce the system uncertainty whereas the measurement on a quantum system will inevitably increase the system uncertainty in turn in fact there is a complicated tradeoff between the uncertainty introduced and the information gained by the measurement on a quantum system to investigate this fundamental problem we will only focus on a typical model of coherent control mode with and without the decoherence term in the paper by establishing some fundamental limits on the performances of both the open loop and measurement based feedback controls we will demonstrate via simulation that the measurement based feedback control of quantum systems is still superior to the open loop control in some sense for the typical model under consideration

reflection symmetries for multiqubit density operators for multiqubit density operators in a suitable tensorial basis we show that a number of nonunitary operations used in the detection and synthesis of entanglement are classifiable as reflection symmetries i e orientation changing rotations while one qubit reflections correspond to antiunitary symmetries as is known for example from the partial transposition criterion reflections on the joint density of two or more qubits are not accounted for by the wigner theorem and are well posed only for sufficiently mixed states one example of such nonlocal reflections is the unconditional not operation on a multiparty density i e an operation yeilding another density and such that the sum of the two is the identity operator this nonphysical operation is admissible only for sufficiently mixed states

impact of positivity and complete positivity on accessibility of markovian dynamics we consider a two dimensional quantum control system evolving under an entropy increasing irreversible dynamics in the semigroup form considering a phenomenological approach to the dynamics we show that the accessibility property of the system depends on whether its evolution is assumed to be positive or completely positive in particular we characterize the family of maps having different accessibilities and show the impact of that property on observable quantities by means of a simple physical model

controllability and simultaneous controllability of isospectral bilinear control systems on complex flag manifolds for isospectral bilinear control systems evolving on the so called complex flag manifolds i e on the orbits of the hermitian matrices under unitary conjugation action it is shown that controllability is almost always verified easy and generic sufficient conditions are provided the result applies to the problem of density operator controllability of finite dimensional quantum mechanical systems in addition we show that systems having different drifts corresponding for example to different larmor frequencies are simultaneously controllable by the same control field

criteria for reachability of quantum states we address the question of which quantum states can be inter converted under the action of a time dependent hamiltonian in particular we consider the problem as applied to mixed states and investigate the difference between pure and mixed state controllabilities introduced in previous work we provide a complete characterization of the eigenvalue spectrum for which the state is controllable under the action of the symplectic group we also address the problem of which states can be prepared if the dynamical lie group is not sufficiently large to allow the system to be controllable

time minimal control of dissipative two level quantum systems the integrable case the objective of this article is to apply recent developments in geometric optimal control to analyze the time minimum control problem of dissipative two level quantum systems whose dynamics is governed by the lindblad equation we focus our analysis on the case where the extremal hamiltonian is integrable

controllability of open quantum systems with kraus map dynamics this paper presents a constructive proof of complete kinematic state controllability of finite dimensional open quantum systems whose dynamics are represented by kraus maps for any pair of states pure or mixed on the hilbert space of the system we explicitly show how to construct a kraus map that transforms one state into another moreover we prove by construction the existence of a kraus map that transforms all initial states into a predefined target state such a process may be used for example in quantum information dilution thus in sharp contrast to unitary control kraus map dynamics allows for the design of controls which are robust to variations in the initial state of the system the capabilities of non unitary control for population transfer between pure states illustrated for an example of a two level system by constructing a family of non unitary kraus maps to transform one pure state into another the problem of dynamic state controllability of open quantum systems i e controllability of state to state transformations given a set of available dynamical resources such as coherent controls incoherent interactions with the environment and measurements is also discussed

controllability of quantum mechanical systems by root space decomposition of su n the controllability property of the unitary propagator of an n level quantum mechanical system subject to a single control field is described using the structure theory of semisimple lie algebras sufficient conditions are provided for the vector fields in a generic configuration as well as in a few degenerate cases