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Quantum networks play a key role in many scenarios of quantum information theory. Here we consider the quantum causal networks in the manner of entropy. First we present a revised smooth max-relative entropy of quantum combs, then we…
The maximum entropy principle, as applied to quantum systems, is a fundamental prescript positing that for a quantum system for which we only have partial knowledge, the maximum entropy state consistent with the partial knowledge is a…
The von Neumann entropy plays a vital role in quantum information theory. The von Neumann entropy determines, e.g., the capacities of quantum channels. Also, entropies of composite quantum systems are important for future quantum networks,…
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 process tomography, the standard procedure to characterize any quantum channel in nature, is affected by a circular argument: in order to characterize the channel, the tomographic preparation and measurement need in turn to be…
The maximum rates for information transmission through noisy quantum channels has primarily been developed for memoryless channels, where the noise on each transmitted state is treated as independent. Many real world communication channels…
We consider compound as well as arbitrarily varying classical-quantum channel models. For classical-quantum compound channels, we give an elementary proof of the direct part of the coding theorem. A weak converse under average error…
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…
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…
Quantum communication theory explores the implications of quantum mechanics to the tasks of information transmission. Many physical channels can be formally described as quantum Gaussian operations acting on bosonic quantum states.…
Quantum filtering is a signal processing technique that estimates the posterior state of a quantum system under continuous measurements and has become a standard tool in quantum information processing, with applications in quantum state…
Quantum resource theories have been widely studied to systematically characterize the non-classicality of quantum systems. Most resource theories focus on quantum states and study their interconversions. Although quantum channels are…
Complete positivity is a ubiquitous assumption in the study of quantum systems interacting with the environment, but the lack of complete positivity of a quantum evolution (called the "negativity") can be used as a measure of the…
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…
A generic qubit unitary operator affected by quantum noise is duplicated and inserted in a coherently superposed channel, superposing two paths offered to a probe qubit across the noisy unitary, and driven by a control qubit. A…
Quantum supermaps are a higher-order generalization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive, trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By…
The quantum capacity of a quantum channel captures its capability for noiseless quantum communication. It lies at the heart of quantum information theory. Unfortunately, our poor understanding of nonadditivity of coherent information makes…
One of most important issues in quantum information theory concerns transmission of information through noisy quantum channels. We discuss few channel characteristics expressed by means of generalized entropies. Such characteristics can…
There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty…
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…