arXiv subjects
Publications and source records attributed to Dariusz Chruściński.
A method is discussed to analyze the dynamics of a dissipative quantum system. The method hinges upon the definition of an alternative (time-dependent) product among the observables of the system. In the long time limit this yields a contracted algebra. This contraction irreversibly affects some of the quantum features of the dissipative system.
A thorough analysis of the evolutions of bipartite systems characterized by the \lq effective absence\rq\, of interaction between the two subsystems is reported. First, the connection between the concepts underlying Interaction-Free Evolutions (IFE) and Decoherence-Free Subspaces (DFS) is explored, showing intricate relations between these concepts. Second, starting from this analysis and inspired by a generalization of DFS already known in the literature, we introduce the notion of generalized IFE (GIFE), also providing a useful characterization that allows to develop a general scheme for finding GIFE states.
We analyze qubit decoherence in the framework of geometric quantum mechanics. In this framework the qubit density operators are represented by probability distributions which are also the Kähler functions on the Bloch sphere. Interestingly, the complete positivity of the quantum evolution is recovered as ellipticity of the second order differential operator (deformed Laplacian) which governs the evolution of the probability distribution.
The generalization of the concept of interaction-free evolutions (IFE) [A. Napoli, {\it et al.}, Phys. Rev. A {\bf 89}, 062104 (2014)] to the case of time-dependent Hamiltonians is discussed. It turns out that the time-dependent case allows for much more rich structures of interaction-free states and interaction-free subspaces. The general condition for the occurrence of IFE is found and exploited to analyze specific situations. Several examples are presented, each one associated to a class of Hamiltonians with specific features.
We analyze random unitary evolution of the qubit within memory kernel approach. We provide sufficient conditions which guarantee that the corresponding memory kernel generates physically legitimate quantum evolution. Interestingly, we are able to recover several well known examples and generate new classes of nontrivial qubit evolution. Surprisingly, it turns out that quantum evolution with memory kernel generated by our approach gives rise to vanishing non-Markovianity measure based on the distinguishability of quantum states.
An interaction free evolving state of a closed bipartite system composed of two interacting subsystems is a generally mixed state evolving as if the interaction were a c-number. In this paper we find the characteristic equation of states possessing similar properties for a bipartite systems governed by a linear dynamical equation whose generator is sum of a free term and an interaction term. In particular in the case of a small system coupled to its environment, we deduce the characteristic equation of decoherence free states namely mixed states evolving as if the interaction term were effectively inactive. Several examples illustrate the applicability of our theory in different physical contexts.
We provide a further analysis of the class of positive maps proposed ten years ago by Kossakowski. In particular we propose a new parametrization which reveals an elegant geometric structure and an interesting interplay between group theory and a certain class of positive maps.
We study a model of a quantum spin register interacting with an environment of spin particles in quantum-measurement limit. In the limit of collective decoherence we obtain the form of state vectors that constitute high-dimensional decoherence-free subspaces (DFS). In a more general setting we present sufficient and necessary conditions for existence of low-dimensional DFSs that can be used to construct subspaces of higher dimension.
We analyze the non-Markovianity degree for random unitary evolution of d-level quantum systems. It is shown how non-Markovianity degree is characterized in terms of local decoherence rates. In particular we derive a sufficient condition for vanishing of the back ow of information.
We provide a class of Bell diagonal entanglement witnesses displaying an additional local symmetry -- a maximal commutative subgroup of the unitary group U(n). Remarkably, this class of witnesses is parameterized by a torus being a maximal commutative subgroup of an orthogonal group SO(n-1). It is shown that a generic element from the class defines an indecomposable entanglement witness. The paper provides a geometric perspective for some aspects of the entanglement theory and an interesting interplay between group theory and block-positive operators.
From the physical point of view entanglement witnesses define a universal tool for analysis and classification of quantum entangled states. From the mathematical point of view they provide highly nontrivial generalization of positive operators and they find elegant correspondence with the theory of positive maps in matrix algebras. We concentrate on theoretical analysis of various important notions like (in)decomposability, atomicity, optimality, extremality and exposedness. Several methods of construction are provided as well. Our discussion is illustrated by many examples enabling the reader to see the intricate structure of these objects. It is shown that the theory of entanglement witnesses finds elegant geometric formulation in terms of convex cones and related geometric structures.
We propose a new characterization of non-Markovian quantum evolution based on the concept of non-Markovianity degree. It provides an analog of a Schmidt number in the entanglement theory and reveals the formal analogy between quantum evolution and the entanglement theory: Markovian evolution corresponds to a separable state and non-Markovian one is further characterized by its degree. It enables one to introduce a non-Markovinity witness -- an analog of an entanglement witness -- and a family of measures -- an analog of Schmidt coefficients -- and finally to characterize maximally non-Markovian evolution being an analog of maximally entangled state. Our approach allows to classify the non-Markovianity measures introduced so far in a unified rigorous mathematical framework.
We present a basic introduction to the dynamics of open quantum systems based on local-in-time master equations. We characterize the properties of time-local generators giving rise to legitimate completely positive trace preserving quantum evolutions. The analysis of Markovian and non-Markovian quantum dynamics is presented as well. The whole discussion is illustrated by the family of many instructive examples.
We provide a recurrent construction of entanglement witnesses for a bipartite systems living in a Hilbert space corresponding to $2N$ qubits ($N$ qubits in each subsystem). Our construction provides a new method of generalization of the Robertson map that naturally meshes with $2N$ qubit systems, i.e., its structure respects the $2^{2N}$ growth of the state space. We prove that for $N>1$ these witnesses are indecomposable and optimal. As a byproduct we provide a new family of PPT (Positive Partial Transpose) entangled states.
We disprove the conjecture that structural physical approximations to optimal entanglement witnesses are separable states. The conjecture holds true for extremal decomposable entanglement witnesses.
We provide a new approach to open quantum systems which is based on the Feshbach projection method in an appropriate Hilbert space. Instead of looking for a master equation for the dynamical map acting in the space of density operators we provide the corresponding equation for the evolution in the Hilbert space of the system. Its solution enables one to construct a legitimate quantum evolution (completely positive and trace preserving). The big advantage of this approach is the ability of performing a consistent approximation which creates notorious problems in the standard Nakajima-Zwanzig approach. The new scheme is illustrated by well known spin-boson model beyond rotating wave approximation.
Using the quantum analog of conditional probability and classical Bayes theorem we discuss some aspects of quantum-classical and classical-classical channels in connection to the recent paper J. Korbicz, P. Horodecki, and R. Horodecki, "Quantum-correlation breaking channels, broadcasting scenarios, and finite Markov chains". Applying the quantum analog of Perron-Frobenius theorem we generalize the result of Korbicz et. al. on full and spectrum broadcasting from quantum-classical channels to arbitrary channels.
We analyze a class of positive partial transpose states (PPT) such that the positivity of its partial transposition is recognized with respect to canonical factorization of the original density operator (Cholesky block decomposition). We call such PPT states strong PPT states (SPPT). This property, contrary to PPT, is basis dependent. It is shown that there exists a proper subset of SPPT states which are separable and provide a separable decomposition for any of these states.