Related papers: Characteristic Operator Functions for Quantum Inpu…
This paper is concerned with a linear fractional representation approach to the synthesis of linear coherent quantum controllers for a given linear quantum plant. The plant and controller represent open quantum harmonic oscillators and are…
In the present paper we study description of Kadison-Schwarz type quantum quadratic operators acting from $\bm_2(\mathbb{C})$ into $\bm_2(\mathbb{C})\o\bm_2(\mathbb{C})$. Note that such kind of operator is a generalization of quantum…
Characteristic functions of linear operators are analytic functions that serve as complete unitary invariants. Such functions, as long as they are built in a natural and canonical manner, provide representations of inner functions on a…
Quantum computation is an attractive front for many problems that are intractable for computers today. One such problem is nonadiabatic quantum molecular dynamics, where quantized internal states coupling to parameterized modes result in a…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
We introduce a general definition of a quantum committor in order to clarify reaction mechanisms and facilitate control in processes where coherent effects are important. With a quantum committor, we generalize the notion of a transition…
Based on a quantum mechanical approach, we investigate moment- (or M-) indeterminate probability densities by way of the characteristic function and self-adjoint operators. The approach leads to new methods to construct classes of…
Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with nonnegative entries. Based on this point of…
We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account…
The presence of correlations in the input state of a non-interacting many-body quantum system can lead to an increase in the amount of work we can extract from it under global unitary processes (ergotropy). The present work explore such…
This paper introduces the class of grey-scale image stack operators as those that (a) map binary-images into binary-images and (b) commute on average with cross-sectioning. Equivalently, stack operators are 1-Lipchitz extensions of set…
An input-output model of a two-level quantum system in the Heisenberg picture is of bilinear form with constant system matrices, which allows the introduction of the concepts of controllability and observability in analogy with those of…
In quantum field theory, the rigorous construction of local observables in the presence of nontrivial interaction is a crucial problem. In a class of integrable quantum field theories, a very abstract existence proof has recently been given…
A quantum characteristic exponent may be defined, with the same operational meaning as the classical Lyapunov exponent when the latter is expressed as a functional of densities. Existence conditions and supporting measure properties are…
In the design of quantum computing devices of the future the basic element is the qubit. It is a two-level quantum system which may describe population transfer from one steady-state to another controlled by a coherent laser field. A…
Implementing general functions of operators is a powerful tool in quantum computation. It can be used as the basis for a variety of quantum algorithms including matrix inversion, real and imaginary-time evolution, and matrix powers. Quantum…
We offer a clear physical explanation for the emergence of the quantum operator formalism, by revisiting the role of the vacuum field in quantum mechanics. The vacuum or random zero-point radiation field has been shown previously, using the…
We study linear problems of mathematical physics in which the adiabatic approximation is used in the wide sense. Using the idea that all these problems can be treated as problems with operator-valued symbol, we propose a general regular…
We propose a scheme for data-driven parameterization of unresolved dimensions of dynamical systems based on the mathematical framework of quantum mechanics and Koopman operator theory. Given a system in which some components of the state…
The correlation structure of multitime quantum processes - succinctly described by quantum combs - is an important resource for many quantum information protocols and control tasks. Inspired by approaches for quantum states, we introduce…