Related papers: On Entropy Transmission for Quantum Channels
What would be a reasonable definition of the conditional entropy of bipartite quantum processes, and what novel insight would it provide? We develop this notion using four information-theoretic axioms and define the corresponding…
The measured relative entropies of quantum states and channels find operational significance in quantum information theory as achievable error rates in hypothesis testing tasks. They are of interest in the near term, as they correspond to…
We investigate the lower bound of the amount of entanglement for faithfully teleporting a quantum state belonging to a subset of the whole Hilbert space. Moreover, when the quantum state belongs to a set composed of two states, a…
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…
Long-distance optical quantum channels are necessarily lossy, leading to errors in transmitted quantum information, entanglement degradation and, ultimately, poor protocol performance. Quantum states carrying information in the channel can…
Quantum channels, a subset of quantum maps, describe the unitary and non-unitary evolution of quantum systems. We study a generalization of the concept of Pauli maps to the case of multipartite high dimensional quantum systems through the…
Quantitative analysis of discontinuity of basic characteristics of quantum states and channels is presented. First we consider general estimates for discontinuity jump (loss) of the von Neumann entropy for a given converging sequence of…
We study quantum channels with respect to their image, i.e., the image of the set of density operators under the action of the channel. We first characterize the set of quantum channels having polytopic images and show that additivity of…
Quantum technology is progressing towards fast quantum control over systems interacting with small environments. Hence such technologies are operating in a regime where the environment remembers the system's past, and the applicability 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…
In this work we prove that the possibility of superactivation of quantum channel capacities is determined by the mathematical properties of the quantum relative entropy function. Before our work this fundamental and purely mathematical…
This article provides an elementary introduction to Gaussian channels and their capacities. We review results on the classical, quantum, and entanglement assisted capacities and discuss related entropic quantities as well as additivity…
This paper investigates the interplay between the properties of quantum states on the Hilbert space \(\ell_2(\kappa)\) and the set-theoretic nature of the cardinal $\kappa$. We focus on the existence of singular $\sigma$-additive states~ --…
An elementary introduction into algebraic approach to unified quantum information theory and operational approach to quantum entanglement as generalized encoding is given. After introducing compound quantum state and two types of…
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…
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'…
The quantum entropy-typical subspace theory is specified. It is shown that any mixed state with von Neumann entropy less than h can be preserved approximately by the entropy-typical subspace with entropy= h. This result implies an universal…
A quantum channel is sufficient with respect to a set of input states if it can be reversed on this set. In the approximate version, the input states can be recovered within an error bounded by the decrease of the relative entropy under the…
The quantum information transfer between a single photon and a two-level atom is considered as a part of a quantum channel. The channel is a degradable channel even when there are decays of the atomic excited state and the single photon…
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…