Related papers: D-divisible quantum evolution families
In this paper we demonstrate that any Markovian master equation defining a completely positive evolution for a quantum-classical hybrid state can always be written in terms of four basic coupling mechanisms. Each of them is characterized by…
In this paper we revisit an integrable map of the plane which we obtained recently as a two-parameter family of deformed mutations in the cluster algebra of type D$_4$. The rational first integral for this map defines an invariant foliation…
Darwinian evolution requires (i) heritable records, (ii) repeatable copying with variation, and (iii) routine irreversibility. Categorical quantum mechanics (CQM) makes precise why ``copy'' and ``delete'' are not generic quantum operations:…
The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact…
Detectability has been introduced as a generalization of state-estimation properties of discrete event systems studied in the literature. It asks whether the current and subsequent states of a system can be determined based on observations.…
Exploiting the path integral approach al la Batalin and Vilkovisky, we show that any anomaly-free Quantum Field Theory (QFT) comes with a family parametrized by certain moduli space M, which tangent space at the point corresponding to the…
The group scheme of ternary automorphisms of a perfect finite dimensional evolution algebra A is computed. The main advantage of using group schemes is that it allows to apply the Lie functor to determine the Lie algebra of ternary…
In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…
We consider a class of quantum dissipative systems governed by a one parameter completely positive maps on a von-Neumann algebra. We introduce a notion of recurrent and metastable projections for the dynamics and prove that the unit…
We construct a new class of positive indecomposable maps in the algebra of 'd x d' complex matrices. Each map is uniquely characterized by a cyclic bistochastic matrix. This class generalizes a Choi map for d=3. It provides a new reach…
Solvable structures are exploited in order to find families of explicit solutions to evolution PDEs admitting suitable differential constraints. The effectiveness of the method is verified on several explicit examples.
The notion of families of quantum invertible maps ($C^*$-algebra homomorphisms satisfying Podle\'s condition) is employed to strengthen and reinterpret several results concerning universal quantum groups acting on finite quantum spaces. In…
We use quantum diffusive trajectories to prove that the time evolution of two-qubit entanglement under spontaneous emission can be fully characterized by optimal continuous monitoring. We analytically determine this optimal unraveling and…
In this work we introduce the concept of generalized exponential $\mathfrak{D}$-pullback attractor for evolution processes, where $\mathfrak{D}$ is a universe of families in $X$, which is a compact and positively invariant family that…
Using the theory of equitable decompositions it is possible to decompose a matrix $M$ appropriately associated with a given graph. The result is a collection of smaller matrices whose collective eigenvalues are the same as the eigenvalues…
This work presents a complete geometrical characterisation of divisible and indivisible time-evolution at the level of probabilities for systems with two configurations, open or closed. Our new geometrical construction in the space of…
We propose a new wiew on the structure of quantum mechanics and postulate a q-deformed algebra of observables. We find equations of motion for this system, which guarantee a unitary time developement. We solve this equations for simple…
We consider N identical oscillators coupled to a single environment and show that the conditions for the existence of decoherence free subspaces are degeneracy of the oscillator frequencies and separability of the coupling with the…
In this paper, building on a previous analysis [1] of exact diagonalization of the space-discretized evolution operator for the study of properties of non-relativistic quantum systems, we present a substantial improvement to this method. We…
In this survey article we give basic introduction to the theory of quantum families of maps. We begin with a general look at non-commutative (or "quantum") topology. Then we formulate all our results in this language. Existence of quantum…