Related papers: A limit relation for entropy and channel capacity …
This paper provides new insight into the classical problem of determining both the capacity of the discrete-time channel with uniform output quantization and the capacity achieving input distribution. It builds on earlier work by Gallager…
Tight lower and upper bounds on the ratio of relative entropies of two probability distributions with respect to a common third one are established, where the three distributions are collinear in the standard $(n-1)$-simplex. These bounds…
We propose a rigorous derivation of the Bekenstein upper limit for the entropy/information that can be contained by a physical system in a given finite region of space with given finite energy. The starting point is the observation that the…
We show how to determine the maximum and minimum possible values of one measure of entropy for a given value of another measure of entropy. These maximum and minimum values are obtained for two standard forms of probability distribution (or…
The quantum relative entropy is frequently used as a distance, or distinguishability measure between two quantum states. In this paper we study the relation between this measure and a number of other measures used for that purpose,…
Entropies associated with spatial subsystems in conventional local quantum field theories are typically divergent when the spatial regions have boundaries. However, in certain linear combinations of the entropies for various subsystems,…
The coding theorem for the entanglement-assisted communication via infinite-dimensional quantum channel with linear constraint is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and…
We show that the recently discovered universal upper bound on the thermal conductance of a single channel comprising particles obeying arbitrary fractional statistics is in fact a consequence of a more general universal upper bound,…
Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We…
We obtain continuity bounds for basic information characteristics of quantum channels depending on their input dimension (if it is finite) and on the input energy bound (if the input dimension is infinite). We pay a special attention to the…
Landauer's principle provides a link between Shannon's information entropy and Clausius' thermodynamical entropy. We set up here a basic formula for the incremental free energy of a quantum channel, possibly relative to infinite systems,…
Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative $q$-entropy is generally unbounded for $q>1$. Upper bounds on the quantum relative $q$-entropy in terms…
We show that the quantum $\alpha$-relative entropies with parameter $\alpha\in (0,1)$ can be represented as generalized cutoff rates in the sense of [I. Csiszar, IEEE Trans. Inf. Theory 41, 26-34, (1995)], which provides a direct…
In quantum systems, entropy production is typically defined as the quantum relative entropy between two states. This definition provides an upper bound for any flux (of particles, energy, entropy, etc.) of bounded observables, which proves…
For all 1 < p < 2, we demonstrate the existence of quantum channels with non-multiplicative maximal p-norms. Equivalently, the minimum output Renyi entropy of order p of a quantum channel is not additive for all 1 < p < 2. The violations…
Any physical channel of communication offers two potential reasons why its capacity (the number of bits it can transmit in a unit of time) might be unbounded: (1) Infinitely many choices of signal strength at any given instant of time, and…
Consider a binary additive noise channel with noiseless feedback. When the noise is a stationary and ergodic process $\mathbf{Z}$, the capacity is $1-\mathbb{H}(\mathbf{Z})$ ($\mathbb{H}(\cdot)$ denoting the entropy rate). It is shown…
In this paper we fill the gap in previous works by proving the formula for entanglement-assisted capacity of quantum channel with additive constraint (such as bosonic Gaussian channel). The main tools are the coding theorem for…
Bekenstein's conjectured entropy bound for a system of linear size R and energy E, S < 2 pi E R, has counterexamples for many of the ways in which the "system," R, E, and S may be defined. Here new ways are proposed to define these…
We give new upper and lower bounds on the concavity of quantum entropy. Comparisons are given with other results in the literature.