Related papers: Axiomatic Approach to Quantum Superchannels
State transformations in quantum mechanics are described by completely positive maps which are constructed from quantum channels. We call a finest sharp quantum channel a context. The result of a measurement depends on the context under…
We explore complementarity between output and environment of a quantum channel (or, more generally, CP map), making an observation that the output purity characteristics for complementary CP maps coincide. Hence, validity of the…
Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…
Quantum networks offer a unifying set of opportunities and challenges across exciting intellectual and technical frontiers, including for quantum computation, communication, and metrology. The realization of quantum networks composed of…
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…
Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information.…
We analyze qubit channels by exploiting the possibility of representing two-level quantum systems in terms of characteristic functions. To do so, we use functions of non-commuting variables (Grassmann variables), defined in terms of…
We introduce the concept of quasi-inverse of quantum and classical channels, prove general properties of these inverses and determine them for a large class of channels acting in an arbitrary finite dimension. Therefore we extend the…
One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of central importance in the description of a…
Quantum communication relies on the existence of high quality quantum channels to exchange information. In practice, however, all communication links are affected by noise from the environment. Here we investigate the ability of quantum…
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 supermaps are higher-order maps transforming quantum operations into quantum operations. Here we extend the theory of quantum supermaps, originally formulated in the finite dimensional setting, to the case of higher-order maps…
We propose a categorical foundation for the connection between pure and mixed states in quantum information and quantum computation. The foundation is based on distributive monoidal categories. First, we prove that the category of all…
A quantum communication channel can be put to many uses: it can transmit classical information, private classical information, or quantum information. It can be used alone, with shared entanglement, or together with other channels. For each…
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…
We present an "uncertainty principle" for quantum channels, showing a relationship between the dimensions of the range of a channel and the range of its complement. We examine some interesting specific cases, and discuss consequences for…
Quantum amplifier channels are at the core of several physical processes. Not only do they model the optical process of spontaneous parametric down-conversion, but the transformation corresponding to an amplifier channel also describes the…
Degradable quantum channels are an important class of completely positive trace-preserving maps. Among other properties, they offer a single-letter formula for the quantum and the private classical capacity and are characterized by the fact…
We present an alternative framework for quantifying the coherence of quantum channels, which contains three conditions: the faithfulness, nonincreasing under sets of all the incoherent superchannels and the additivity. Based on the…
Discrimination between objects, in particular quantum states, is one of the most fundamental tasks in (quantum) information theory. Recent years have seen significant progress towards extending the framework to point-to-point quantum…