Related papers: A quantum version of Wielandt's inequality
In this work we design a specific simulation tool for quantum channels which is based on the use of a control system. This allows us to simulate an average quantum channel which is expressed in terms of an ensemble of channels, even when…
We study quantum channels that vary on time in a deterministic way, that is, they change in an independent but not identical way from one to another use. We derive coding theorems for the classical entanglement assisted and unassisted…
This paper introduces a method for calculating the quantum relative entropy of channels, an essential quantity in quantum channel discrimination and resource theories of quantum channels. By building on recent developments in the…
The primary objective of quantum Shannon theory is to evaluate the capacity of quantum channels. In spite of the existence of rigorous coding theorems that quantify the transmission of information through quantum channels, superadditivity…
Capacities of quantum channels are fundamental quantities in the theory of quantum information. A desirable property is the additivity for a capacity. However, this cannot be achieved for a few quantities that have been established as…
The capacity of quantum channel with product input states was formulated by the quantum coding theorem. However, whether entangled input states can enhance the quantum channel is still open. It turns out that this problem is reduced to…
It is known that the overlap of two energy eigenstates in a decaying quantum system is bounded from above by a function of the energy detuning and the individual decay rates. This is usually traced back to the positive definiteness of an…
We introduce and study norms in the space of hermitian operators, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum…
We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups $G$. Beginning with a…
We prove boundedness results for the injectivity regions for PEPS. Our result is a higher-dimensional generalization of the quantum Wielandt inequality.
The mathematical structure of quantum entanglement is studied and classified from the point of view of quantum compound states. We show that t he classical-quantum correspondences such as encodings can be treated as dia gonal (d-)…
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…
The more than thirty years old issue of the (classical) information capacity of quantum communication channels was dramatically clarified during the last years, when a number of direct quantum coding theorems was discovered. The present…
Channel-state duality is a central result in quantum information science. It refers to the correspondence between a dynamical process (quantum channel) and a static quantum state in an enlarged Hilbert space. Since the corresponding dual…
In this work, we prove a lower bound on the difference between the first and second singular values of quantum channels induced by random isometries, that is tight in the scaling of the number of Kraus operators. This allows us to give an…
Incompatible quantum channels cannot be jointly and exactly realized, meaning that any approximate joint realization inevitably entails a tradeoff in implementation accuracy. While this notion of channel incompatibility unifies fundamental…
A quantum inequality for the quantized electromagnetic field is developed for observers in static curved spacetimes. The quantum inequality derived is a generalized expression given by a mode function expansion of the four-vector potential,…
We prove new quantitative limitations on any approximate simultaneous cloning or broadcasting of mixed states. The results are based on information-theoretic (entropic) considerations and generalize the well known no-cloning and…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
We introduce a new aspect of nonlocality which arises when the task of quantum states distinguishability is considered under local operations and shared entanglement in the absence of classical communication. We find the optimal amount of…