相关论文: On the Input-Degradedness and Input-Equivalence Be…
The ordering of communication channels was first introduced by Shannon. In this paper, we aim to find a characterization of the Shannon ordering. We show that $W'$ contains $W$ if and only if $W$ is the skew-composition of $W'$ with a…
A channel is degradable if there exists a second channel that maps the output state of the channel to the environment state. These channels satisfy the property that the output state contains more information about the input than the…
A quantum analogue of the famous Blackwell Theorem in classical statistics has recently been proposed. Given two quantum channels A and B, a set of payoff functions have been proven to have values for B at least as high as they are for A if…
Two partial orderings among communication channels, namely, `being degradable into' and `being less noisy than,' are reconsidered in the light of recent results about statistical comparisons of quantum channels. Though our analysis covers…
For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by post-processings of the other channel can be characterized by comparing the success probabilities for the two…
For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by post-processings of the other channel can be characterized by comparing the success probabilities for the two…
For any given channel $W$ with classical inputs and possibly quantum outputs, a dual classical-input channel $W^\perp$ can be defined by embedding the original into a channel $\mathcal N$ with quantum inputs and outputs. Here we give new…
It is shown that given two copies of a q-ary input channel $W$, where q is prime, it is possible to create two channels $W^-$ and $W^+$ whose symmetric capacities satisfy $I(W^-)\le I(W)\le I(W^+)$, where the inequalities are strict except…
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…
A group of transition probability functions form a Shannon's channel whereas a group of truth functions form a semantic channel. Label learning is to let semantic channels match Shannon's channels and label selection is to let Shannon's…
The quantization of the output of a binary-input discrete memoryless channel to a smaller number of levels is considered. An algorithm which finds an optimal quantizer, in the sense of maximizing mutual information between the channel input…
We study the optimal rates of emulation (also called interconversion) between quantum channels. When the source and the target channels are idempotent, we give a single-letter expression for the zero-error emulation capacity in terms of…
Two channels are equivalent if their maximum likelihood (ML) decoders coincide for every code. We show that this equivalence relation partitions the space of channels into a generalized hyperplane arrangement. With this, we define a coding…
We connect two key concepts in quantum information: compatibility and divisibility of quantum channels. Two channels are compatible if they can be both obtained via marginalization from a third channel. A channel divides another channel if…
We develop the notion of a locally homomorphic channel and prove an approximate equivalence between those and codes for computing functions. Further, we derive decomposition properties of locally homomorphic channels which we use to analyze…
Divergence chain rules for channels relate the divergence of a pair of channel inputs to the divergence of the corresponding channel outputs. An important special case of such a rule is the data-processing inequality, which tells us that if…
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…
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,…
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…
We consider transmitting a source across a pair of independent, non-ergodic channels with random states (e.g., slow fading channels) so as to minimize the average distortion. The general problem is unsolved. Hence, we focus on comparing two…