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We consider energy-constrained infinite-dimensional quantum channels from a given system (satisfying a certain condition) to any other systems. We show that dealing with basic capacities of these channels we may assume (accepting…
In this work we analyze properties of generic quantum channels in the case of large system size. We use random matrix theory and free probability to show that the distance between two independent random channels converges to a constant…
The classical randomization criterion is an important result of statistical decision theory. Recently, a quantum analogue has been proposed, giving equivalent conditions for two sets of quantum states, ensuring existence of a quantum…
We prove that a broad array of capacities of a quantum channel are continuous. That is, two channels that are close with respect to the diamond norm have correspondingly similar communication capabilities. We first show that the classical…
We address the question of the existence of quantum channels that are divisible in two quantum channels but not in three or, more generally, channels divisible in $n$ but not in $n+1$ parts. We show that for the qubit those channels…
Let $K$ be a convex subset of the state space of a finite dimensional $C^*$-algebra. We study the properties of channels on $K$, which are defined as affine maps from $K$ into the state space of another algebra, extending to completely…
We examine the dispersion of Brownian particles in a symmetric two dimensional channel, this classical problem has been widely studied in the literature using the so called Fick-Jacobs' approximation and its various improvements. Most…
The dynamics of quantum systems are generally described by a family of quantum channels (linear, completely positive and trace preserving maps). In this note, we mainly study the range of all possible values of…
By using the Choi-Jamio{\l}kowski isomorphism, we propose two classes of coherence monotones of quantum channels based on the unified $(r,s)$-relative entropy and the sandwiched R\'{e}nyi relative entropy. Elegant properties of the…
We provide new results for computing and comparing the quantum gate fidelity of quantum channels via their Choi matrices. We extend recent work that showed there exist non-dual pairs of quantum channels with equal gate fidelity by providing…
A classification of one-mode Gaussian channels is given up to canonical unitary equivalence. A complementary to the quantum channel with additive classical Gaussian noise is described providing an example of one-mode Gaussian channel which…
In this paper, we introduce a generalised diagonal dimension. We explain why the generalised diagonal dimension extends the notion of diagonal dimension defined by Li, Liao, and Winter, and under which conditions these dimensions coincide.…
We show that the canonical equivalences of categories between 2-dimensional (unoriented) topological quantum field theories valued in a symmetric monoidal category and (extended) commutative Frobenius algebras in that symmetric monoidal…
Quantum channels, which are completely positive and trace preserving mappings, can alter the dimension of a system; e.g., a quantum channel from a qubit to a qutrit. We study the convex set properties of dimension-altering quantum channels,…
We identify and characterize all the local quantum channels that preserves the set of classical states, i.e., does not create any quantum correlations. At first we show that the quantum correlations cannot be created from without if and…
In this paper, we consider the convex set of $d$ dimensional unital quantum channels. In particular, we parametrise a family of maps and through this parametrisation we provide a partial characterisation of the set of unital quantum maps…
We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible'…
Quantum channels describe the most general dynamics of open quantum systems. A quantum channel, as a linear map on vectorized quantum states, can be represented by a single matrix, whose spectrum is called the channel spectrum. Here we…
Two quantum channels are called compatible if they can be obtained as marginals from a single broadcasting channel; otherwise they are incompatible. We derive a characterization of the compatibility relation in terms of concatenation and…
We investigate the set of quantum channels acting on a single qubit. We provide an alternative, compact generalization of the Fujiwara-Algoet conditions for complete positivity to non-unital qubit channels, which we then use to characterize…