Related papers: The inverse eigenvalue problem for quantum channel…
Call a spectrum of Hamiltonian sparse if each eigenvalue can be quickly restored with accuracy $\epsilon$ from its rough approximation in within $\epsilon_1$ by means of some classical algorithm. It is shown how a behavior of system with…
In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant…
We study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$. If the graph is "straight", i.e. periodic…
We study the inverse problem of constructing an appropriate Hamiltonian from a physically reasonable set of orthogonal wave functions for a quantum spin system. Usually, we are given a local Hamiltonian and try to characterize the relevant…
In this paper, the quantum spectrum of isochronous potentials is investigated. Given that the frequency of the classical motion in such potentials is energy-independent, it is natural to expect their quantum spectra to be equispaced.…
The recent discovery of fully-homomorphic classical encryption schemes has had a dramatic effect on the direction of modern cryptography. Such schemes, however, implicitly rely on the assumptions that solving certain computation problems…
A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence ``atemporal''). It can be used to relate quantum dynamical…
We establish that a perfect-transmission scattering problem can be described by a class of parity and time reversal symmetric operators and hereby we provide a scenario for understanding and implementing the corresponding quasi-Hermitian…
We investigate the peripheral spectrum of irreducible positive elements of an ordered Banach algebra. In particular, we give conditions under which the peripheral spectrum contains (or coincides with) the cyclic group generated by a root of…
Quantum channels, a subset of quantum maps, describe the unitary and non-unitary evolution of quantum systems. We study a generalization of the concept of Pauli maps to the case of multipartite high dimensional quantum systems through the…
The task of determining whether a given quantum channel has positive capacity to transmit quantum information is a fundamental open problem in quantum information theory. In general, the coherent information needs to be computed for an…
The exact meaning of the noise spectrum of eigenvalues of the covariance matrix is discussed. In order to better understand the possible phenomena behind the observed noise, the spectrum of eigenvalues of the covariance matrix is studied…
In recent years, new algorithms and cryptographic protocols based on the laws of quantum physics have been designed to outperform classical communication and computation. We show that the quantum world also opens up new perspectives in the…
Recently it was shown that the main distinguishing features of quantum mechanics (QM) can be reproduced by a model based on classical random fields, so called prequantum classical statistical field theory (PCSFT). This model provides a…
For many completely positive maps repeated compositions will eventually become entanglement breaking. To quantify this behaviour we develop a technique based on the Schmidt number: If a completely positive map breaks the entanglement with…
We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to…
The interior transmission eigenvalue problem (ITP) plays a central role in inverse scattering theory and in the spectral analysis of inhomogeneous media. Despite its smooth dependence on the refractive index at the PDE level, the…
We provide a new characterisation of quantum supermaps in terms of an axiom that refers only to sequential and parallel composition. Consequently, we generalize quantum supermaps to arbitrary monoidal categories and operational…
Front form dynamics is not a manifestly rotational invariant formalism. In particular, the requirement of an invariance under rotations around the transverse axes is difficult to fulfill.In the present work it is investigated, to which…
The requirement that the quantum partition function be invariant under a renormalization group transformation results in a wide class of exact renormalization group equations, differing in the form of the kernel. Physical quantities should…