相关论文: Maps and inverse maps in open quantum dynamics
For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…
We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…
In this paper, a characterization of maps between quantum states that preserve pure states and strict convex combinations is obtained. Based on this characterization, a structural theorem for maps between multipartite quantum states that…
Valid transformations between quantum states are necessarily described by completely positive maps, instead of just positive maps. Positive but not completely positive maps such as the transposition map cannot be implemented due to the…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
Markovianity of the quantum open system processes is a topic of the considerable current interest. Typically, invertibility is assumed to be non-essential for Markovianity of the open-quantum-system dynamical maps. Nevertheless, in this…
In this paper, we discuss positive maps induced by (irreducibly) covariant linear operators for finite groups. The application of group theory methods allows deriving some new results of a different kind. In particular, a family of…
An element of a group is \emph{reversible} if it is conjugate to its own inverse, and it is \emph{strongly reversible} if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be…
A precise meaning is given to the notion of continuous iteration of a mapping. Usual discrete iterations are extended into a dynamical flow which is a homotopy of them all. The continuous iterate reveals that a dynamical map is formend by…
Complete positivity of quantum dynamics is often viewed as a litmus test for physicality, yet it is well known that correlated initial states need not give rise to completely positive evolutions. This observation spurred numerous…
We use the inverse pressure concept to estimate the stable dimension for hyperbolic non-invertible maps which are conformal in the stable fibers. The non-invertible case is different than the diffeomorphism case. In particular we show that…
We investigate completely positive maps for an open system interacting with its environment. The families of the initial states for which the reduced dynamics can be described by a completely positive map are identified within the framework…
The well-known theory of "rational canonical form of an operator" describes the invariant factors, or elementary divisors, as a complete set of invariants of a similarity class of an operator on a finite-dimensional vector space $\V$ over a…
We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose…
We analyze the structure of the subset of states generated by unital completely positive quantum maps, A witness that certifies that a state does not belong to the subset generated by a given map is constructed. We analyse the…
In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital $C^*$-algebras, with a particular focus on gapped maps for…
Quantum entanglement is an important phenomenon in quantum information theory. To detect entanglement theoretically, positive but not completely positive maps are used. The Kadison-Schwarz (KS) inequality interpolates between positivity and…
We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum $\chi_\alpha^2$-divergence for some $\alpha \in…
We present positive maps and matrix inequalities for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps that are in one-to-one…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…