Related papers: A limit relation for entropy and channel capacity …
In this paper we seek to understand what current knowledge of entanglement entropies suggests about the appropriate way to interpret the covariant entropy bound. We first begin by arguing that just as in the classical case, a universal…
The novel concept of quantum logical entropy is presented and analyzed. We prove several basic properties of this entropy with regard to density matrices. We hereby motivate a different approach for the assignment of quantum entropy to…
By applying the Heisenberg's uncertainty principle for a macroscopic quantum gas formed by gravitational waves an expression for the universal bound on the entropy proposed by Bekenstein for any system of maximum radius R and total energy E…
So far, there have been plenty of literatures on the metric in the space of probability distributions and quantum states. As for channels, however, only a little had been known. In this paper, we impose monotonicity by concatenation of…
We analyze the quantum capacity of a unital quantum channel, using ideas from the proof of near-optimality of Petz recovery map [Barnum and Knill 2000] and give an upper bound on the quantum capacity in terms of regularized output $2$-norm…
Boundary impurities are known to dramatically alter certain bulk properties of 1+1 dimensional strongly correlated systems. The entanglement entropy of a zero temperature Luttinger liquid bisected by a single impurity is computed using a…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
In this paper we show how \emph{the metric theory of tensor products} developed by Grothendieck perfectly fits in the study of channel capacities, a central topic in \emph{Shannon's information theory}. Furthermore, in the last years…
In this article, we generalize a proof technique by Alicki, Fannes and Winter and introduce a method to prove continuity bounds for entropic quantities derived from different quantum relative entropies. For the Umegaki relative entropy, we…
We study the maximum achievable differential entropy at the output of a system assigning to each input X the sum X+N, with N a given noise with probability law absolutely continuous with respect to the Lebesgue measure and where the input…
We consider the question of entropic uncertainty relations for prime power dimensions. In order to improve upon such uncertainty relations for higher dimensional quantum systems, we derive a tight lower bound amount of entropy for multiple…
We prove a lemma which allows one to extend results about the additivity of the minimal output entropy from highly symmetric channels to a much larger class. A similar result holds for the maximal output $p$-norm. Examples are given showing…
Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how fundamental concepts…
As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a…
We consider the transmission of classical information over a quantum channel by two senders. The channel capacity region is shown to be a convex hull bound by the Von Neumann entropy and the conditional Von Neumann entropy. We discuss some…
We prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT at high energies for global symmetries associated with finite groups. An equivalent statement, based on the entropic…
By a use of the Fredholm determinant theory, the unified quantum entropy notion has been extended to a case of infinite-dimensional systems. Some of the known (in the finite-dimensional case) basic properties of the introduced unified…
Entropy bounds render quantum corrections to the cosmological constant $\Lambda$ finite. Under certain assumptions, the natural value of $\Lambda$ is of order the observed dark energy density $\sim 10^{-10} {\rm eV}^4$, thereby resolving…
One of the fundamental tasks in quantum information processing is to measure the quantum channels. Similar to measurements of quantum states, measurements of quantum channels are inherently stochastic, that is, quantum theory provides a…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…