Related papers: Affine maps of density matrices
We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that…
For a prototype quadratic Hamiltonian describing a driven, dissipative system, exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is…
By using the properties of orthogonal polynomials, we present an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that describes a…
A system interacting with its environment will give rise to a quantum evolution. After tracing over the environment the net evolution of the system can be described by a linear Hermitian map. It has recently been shown that a necessary and…
We show that a positive linear map preserves local continuity (convergence) of the entropy if and only if it preserves finiteness of the entropy, i.e. transforms operators with finite entropy to operators with finite entropy. The last…
Many models of population dynamics are formulated as deterministic iterated maps although real populations are stochastic. This is justifiable in the limit of large population sizes, as the stochastic fluctuations are negligible then.…
We determine the structure of linear maps on complex (real) square matrices sending unitary (orthogonal) matrices to multiples of unitary (orthogonal) matrices. The result is used to determine the linear preservers of matrix pairs…
The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their…
Here we consider piecewise fractional linear maps with three branches. The paper presents a study of invariant measures with densities which can be written as infinite series. These series either have infinitely many poles or they sum up to…
We propose a transformation algorithm for a class of Linear Parameter-Varying (LPV) systems with functional affine dependence on parameters, where the system matrices depend affinely on nonlinear functions of the scheduling varable, into…
Normalizing flows attempt to model an arbitrary probability distribution through a set of invertible mappings. These transformations are required to achieve a tractable Jacobian determinant that can be used in high-dimensional scenarios.…
A new method of analysing positive bistochastic maps on the algebra of complex matrices $M_{3}$ has been proposed. By identifying the set of such maps with a convex set of linear operators on $\mathbb{R}^{8}$, one can employ techniques from…
We present and compare two families of ensembles of random density matrices. The first, static ensemble, is obtained foliating an unbiased ensemble of density matrices. As criterion we use fixed purity as the simplest example of a useful…
The quantum density matrix generalises the classical concept of probability distribution to quantum theory. It gives the complete description of a quantum state as well as the observable quantities that can be extracted from it. Its…
The intrinsic nature of a problem usually suggests a first suitable method to deal with it. Unfortunately, the apparent ease of application of these initial approaches may make their possible flaws seem to be inherent to the problem and…
Quantum computing has the potential to significantly speed up complex computational tasks, and arguably the most promising application area for near-term quantum computers is the simulation of quantum mechanics. To make the most of our…
Eigenvalue-preserving-but-not-completely-eigenvalue-preserving (EnCE) maps were previously introduced for the purpose of detection and quantification of nonclassical correlation, employing the paradigm where nonvanishing quantum discord…
We develop the HJM framework for forward rates driven by affine processes on the state space of symmetric positive matrices. In this setting we find a representation for the long-term yield and investigate the yield's asymptotic behaviour.
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…
A new notion of thickness for subsets of $B[0,1]\subset \mathbb{R}^n$ called affine thickness is defined; this notion of thickness is a generalisation of Falconer-Yavicoli thickness and is adapted to be used in the study of certain sets…