Related papers: Dividing Quantum Channels
We present a method to detect properties of quantum channels, assuming that some a priori information about the form of the channel is available. The method is based on a correspondence with entanglement detection methods for multipartite…
Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a…
Quantum channels can describe all transformations allowed by quantum mechanics. We provide an explicit universal protocol to construct all possible quantum channels, using a single qubit ancilla with quantum non-demolition readout and…
The quantum capacity of degradable quantum channels has been proven to be additive. On the other hand, there is no general rule for the behavior of quantum capacity for non-degradable quantum channels. We introduce the set of partially…
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…
We study quantum channels with respect to their image, i.e., the image of the set of density operators under the action of the channel. We first characterize the set of quantum channels having polytopic images and show that additivity of…
This paper provides a characterization for the set of antidegradable qubit channels. The characterization arises from the correspondence between the antidegradability of a channel and the symmetric extendibility of its Choi operator. Using…
We study dynamical semigroups of positive, but not completely positive maps on finite-dimensional bipartite systems and analyze properties of their generators in relation to non-decomposability and bound-entanglement. An example of…
The set of doubly-stochastic quantum channels and its subset of mixtures of unitaries are investigated. We provide a detailed analysis of their structure together with computable criteria for the separation of the two sets. When applied to…
We analyze qubit channels by exploiting the possibility of representing two-level quantum systems in terms of characteristic functions. To do so, we use functions of non-commuting variables (Grassmann variables), defined in terms of…
Quantum masking is a special type of secret sharing in which some information gets reversibly distributed into a multipartite system, leaving the original information inaccessible to each subsystem. This paper proposes a dynamical extension…
We show that the representations of the Cuntz C$^\ast$-algebras $O_n$ which arise in wavelet analysis and dilation theory can be classified through a simple analysis of completely positive maps on finite-dimensional space. Based on this…
Decoherence of quantum systems is described by quantum channels. However, a complete understanding of such channels, especially in the multi-particle setting, is still an ongoing difficult task. We propose the family of quantum maps that…
Two quantum channels are called compatible if they can be obtained as marginals from a single broadcasting channel; otherwise they are incompatible. We derive a characterization of the compatibility relation in terms of concatenation and…
Quantum channels describe subsystem or open system evolution. Using the classical Koopman operator that evolves functions on phase space, 4 classical Koopman channels are identified that are analogs of the 4 possible quantum channels in a…
We introduce the concept of quasi-inverse of quantum and classical channels, prove general properties of these inverses and determine them for a large class of channels acting in an arbitrary finite dimension. Therefore we extend the…
Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number of a quantum channel. It enables one to define classes of quantum channels which partially break quantum entanglement.…
Phase covariant qubit dynamics describes an evolution of a two-level system under simultaneous action of pure dephasing, energy dissipation, and energy gain with time-dependent rates $\gamma_z(t)$, $\gamma_-(t)$, and $\gamma_+(t)$,…
Let L(m,n) denote the convex set of completely positive trace preserving operators from C^{m x m} to C^{n x n}$, i.e quantum channels. We give a necessary condition for L in L(m,n) to be an extreme point. We show that generically, this…
In this paper we give a simple sequence of necessary and sufficient finite dimensional conditions for a positive map between certain subspaces of bounded linear operators on separable Hilbert spaces to be completely positive. These…