Related papers: The semigroup structure of Gaussian channels
In this paper, we study the multiplicative behaviour of quantum channels, mathematically described by trace preserving, completely positive maps on matrix algebras. It turns out that the multiplicative domain of a unital quantum channel has…
We investigate various groupoids associated to an arbitrary inverse semigroup with zero. We show that the groupoid of filters with respect to the natural partial order is isomorphic to the groupoid of germs arising from the standard action…
As a common non-trivial generalization of the concept of a proper generalized Bassian group, we introduce the notion of a semi-generalized Bassian group and initiate its comprehensive investigation. Precisely, we give a satisfactory…
We present a method for estimating conditionally Gaussian random vectors with random covariance matrices, which uses techniques from the field of machine learning. Such models are typical in communication systems, where the covariance…
We introduce Partially Coherent Direct Sum (PCDS) quantum channels, as a generalization of the already known Direct Sum quantum channels. We derive necessary and sufficient conditions to identify the subset of those maps which are…
Information theory establishes the ultimate limits on performance for noisy communication systems [Shannon48]. An accurate model of a physical communication device must include quantum effects, but typically including these makes the theory…
We study automaton structures, i.e. groups, monoids and semigroups generated by an automaton, which, in this context, means a deterministic finite-state letter-to-letter transducer. Instead of considering only complete automata, we…
Quantum superchannels are maps whose input and output are quantum channels. Rather than taking the domain to be the space of all linear maps we motivate and define superchannels on the operator system spanned by quantum channels. Extension…
Non-asymptotic quantum Shannon theory analyses how to transmit quantum information across a quantum channel as efficiently as possible within a specified error tolerance, given access to a finite, fixed, number of channel uses. In a recent…
In this paper we introduce EPOSIC channels, a class of SU(2)-covariant quantum channels. We give their definition, a Kraus representation of them, and compute their Choi matrices. We show that these channels form the set of extreme points…
Given an arbitrary group $G$ we construct a semigroup of idempotents (band) $B_G$ with the property that the free idempotent generated semigroup over $B_G$ has a maximal subgroup isomorphic to $G$. If $G$ is finitely presented then $B_G$ is…
The impact of a noisy Gaussian channel on a wide range of non-Gaussian input states is studied in this work. The nonclassical nature of the states, both input and output, is developed by studying the corresponding photon statistics and…
Quantum channels can be mathematically represented as completely positive trace-preserving maps that act on a density matrix. A general quantum channel can be written as a convex sum of `extremal' channels. We show that for an $N$-level…
Quantum channels can be activated by a kind of channels whose quantum capacity is zero. This activation effect might be useful to overcome noise of channels by attaching other channels which can enhance the capacity of a given channel. In…
One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of quantum channel which is a basic building block of any data-transmitting or data-processing…
This work is devoted to the so-called filtration theory of semigroup generators in the unit disk. It should be noted that numerous filtrations studied to nowdays have been introduced for different purposes and considered from different…
We show that the quantum family of all maps from a finite space to a finite dimensional compact quantum semigroup has a canonical quantum semigroup structure.
All the $n(2n+3)$ mean and covariance parameters of an $n$-mode Gaussian states are expressed in terms of the expectation values of the same number of conjugates of the total number observable. This permits a complete tomography of the…
We identify two broad types of noninvertibilities in quantum dynamical maps, one necessarily associated with CP indivisibility and one not so. We study the production of (non-)Markovian, invertible maps by the process of mixing…
Given any covariance matrix corresponding to a so-called pure Gaussian state, a linear quantum system can be designed to achieve the assigned covariance matrix. In most cases, however, one might obtain a system that is difficult to realize…