Related papers: A category theoretic approach to asymptotic quantu…
The set of doubly-stochastic quantum channels and its subset of mixtures of unitaries are investigated. We provide a detailed analysis of their structure together with computable criteria for the separation of the two sets. When applied to…
The Birkhoff's theorem states that any doubly stochastic matrix lies inside a convex polytope with the permutation matrices at the corners. It can be proven that a similar theorem holds for unitary matrices with equal line sums for prime…
The classic Birkhoff- von Neumann theorem states that the set of doubly stochastic matrices is the convex hull of the permutation matrices. In this paper, we study a generalisation of this theorem in the type $II_1$ setting. Namely, we…
It is proved that every doubly stochastic quantum channel that is properly averaged with the completely depolarizing channel can be written as a convex combination of unitary channels. As a consequence, we find that the collection of…
We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups $G$. Beginning with a…
Let B be an n by n doubly substochastic matrix. We show that B can be written as a convex combination of no more than {\sigma}(B)+t subpermutation matrices, where {\sigma}(B) is the number of nonzero elements in B and t is the number of…
The recently introduced random purification channel, which converts $n$ i.i.d. copies of any mixed quantum state into a uniform convex combination of $n$ i.i.d. copies of its purifications, has proved to be an extremely useful tool in…
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 prove new quantitative limitations on any approximate simultaneous cloning or broadcasting of mixed states. The results are based on information-theoretic (entropic) considerations and generalize the well known no-cloning and…
Many quantum information tasks use inputs of the form $\rho^{\otimes m}$, which naturally induce permutation and unitary symmetries. We classify all quantum channels that respect both symmetries - i.e. unitary-equivariant and…
Quantum measurements can be interpreted as a generalisation of probability vectors, in which non-negative real numbers are replaced by positive semi-definite operators. We extrapolate this analogy to define a generalisation of doubly…
In the present paper we show a link between bistochastic quantum channels and classical maps. The primary goal of this work is to analyse the multiplicative structure of the Birkhoff polytope of order 3 (the simplest non-trivial case). A…
Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of…
Every channel can be expressed as a convex combination of deterministic channels with each deterministic channel corresponding to one particular intrinsic state. Such convex combinations are in general not unique, each giving rise to a…
Many important properties of quantum channels are quantified by means of entropic functionals. Characteristics of such a kind are closely related to different representations of a quantum channel. In the Jamio{\l}kowski-Choi representation,…
Quantum channel, as the information transmitter, is an indispensable tool in quantum information theory. In this paper, we study a class of special quantum channels named the mixed-permutation channels. The properties of these channels are…
Any square matrix can be transformed into a doubly stochastic matrix via Sinkhorn scaling with diagonal matrices or completing to a larger dimensional matrix. Standard Birkhoff-von Neumann and Pauli decompositions represent such matrices as…
Let G be a finite subgroup of unitary matrices acting on the space of $N$-qubits. We associate with G a uniform quantum channel QU from the space on $N$-qubits to itself. We give a quantum algorithm to approximate this channel by…
In this work we improve the quantum communication rates of various quantum channels of interest using permutation-invariant quantum codes. We focus in particular on parametrized families of quantum channels and aim to improve bounds on…
Several techniques of generating random quantum channels, which act on the set of $d$-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show under which conditions…