Related papers: Mixing doubly stochastic quantum channels with the…
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…
Being attracted by the property of classical polar code, researchers are trying to find its analogue in quantum fields, which is called quantum polar code. The first step and the key to design quantum polar code is to find out for the…
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…
Since a quantum measurement generally disturbs the state of a quantum system, one might think that it should not be possible for a sender and receiver to communicate reliably when the receiver performs a large number of sequential…
We give a general solution to the question when the convex hulls of orbits of quantum states on a finite-dimensional Hilbert space under unitary actions of a compact group have a non-empty interior in the surrounding space of all density…
We analyze convex combinations of non-unital qubit maps that are phase-covariant. In particular, we consider the behavior of maps that combine amplitude damping, inverse amplitude damping, and pure dephasing. We show that mixing non-unital…
A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output $p$-norm can be…
We study the super dense coding capacity in the presence of quantum channels with correlated noise. We investigate both the cases of unitary and non-unitary encoding. Pauli channels for arbitrary dimensions are treated explicitly. The super…
We provide a generalization of quantum polar codes to quantum channels with qudit-input, achieving the symmetric coherent information of the channel. Our scheme relies on a channel combining and splitting construction, where a two-qudit…
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…
A simple criterion for local equality between the constrained Holevo capacity and the quantum mutual information of a quantum channel is obtained. It implies that the set of all states for which this equality holds is determined by the…
We develop a device-independent framework for testing quantum channels. That is, we falsify a hypothesis about a quantum channel based only on an observed set of input-output correlations. Formally, the problem consists of characterizing…
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…
The L\"uders rule provides a way to define a quantum channel given a quantum measurement. Using this construction, we establish an if-and-only-if condition for the existence of a $d$-dimensional Symmetric Informationally Complete quantum…
Using the axiomatic definition of the coherence measure, such as the $l_{1}$ norm and the relative entropy, we study the phenomena of two-qubit system quantum coherence through quantum channels where successive uses of the channels are…
Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels. Specifically, it is shown that when the input alphabet size is a prime number, a similar construction to that for…
Quantum channels can be described via a unitary coupling of system and environment, followed by a trace over the environment state space. Taking the trace instead over the system state space produces a different mapping which we call the…
We prove the statement "The collection of all elements of $\mathcal S$ which have only simple eigenvalues is dense in $\mathcal S$" for different sets $\mathcal S$, including: all quantum channels, the unital channels, the positive…
Completely depolarising channels are often regarded as the prototype of physical processes that are useless for communication: any message that passes through them along a well-defined trajectory is completely erased. When two such channels…
Recently, a purely quantum version of polar codes has been proposed in [1] based on a quantum channel combining and splitting procedure, where a randomly chosen two-qubit Clifford unitary acts as channel combining operation. Here, we…