Related papers: Multiplicative Properties of Quantum Channels
In this work we examine quantum states which have non-negative amplitudes (in a fixed basis) and the channels which preserve them. These states include the ground states of stoquastic Hamiltonians and they are of interest since they avoid…
We consider a quantum channel acting on an infinite dimensional von Neumann algebra of operators on a separable Hilbert space. When there exists an invariant normal faithful state, the cyclic properties of such channels are investigated…
This work presents a differentiable geometric parameterization of quantum channels in Kraus representation, which can be efficiently probed to find an unknown quantum channel. We explore its feasibility in finding the quasi inverse…
Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic…
We introduce a class of linear maps irreducibly covariant with respect to the finite group generated by the Weyl operators. This group provides a direct generalization of the quaternion group. In particular, we analyze the irreducibly…
A quantum channel is a mapping which sends density matrices to density matrices. The estimation of quantum channels is of great importance to the field of quantum information. In this thesis two topics related to estimation of quantum…
Quantum channels, also called quantum operations, are linear, trace preserving and completely positive transformations in the space of quantum states. Such operations describe discrete time evolution of an open quantum system interacting…
We investigate the quantum privacy properties of an important class of quantum chan-nels, by making use of a connection with Schur product matrix operations and associated correlationmatrix structures. For channels implemented by mutually…
We investigate the structural and dynamical properties of a class of quantum channels on von Neumann algebras induced by averaging over operator groups via the Pettis integral. Utilizing the classical Yosida--Hewitt decomposition, we focus…
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…
Using the known possibility to associate the completely positive maps with density matrices and recent results on expressing the density matrices with sets of classical probability distributions of dichotomic random variables we construct…
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…
We investigate the set of quantum channels acting on a single qubit. We provide an alternative, compact generalization of the Fujiwara-Algoet conditions for complete positivity to non-unital qubit channels, which we then use to characterize…
Several techniques of generating random quantum channels, which act on the set of $d$-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show under which conditions…
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 past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…
Determining whether a noisy quantum channel can be used to reliably transmit quantum information at a non-zero rate is a challenging problem in quantum information theory. This is because it requires computation of the channel's coherent…
In this article, we investigate the additivity phenomenon in the dynamic capacity of a quantum channel for trading classical communication, quantum communication and entanglement. Understanding such additivity property is important if we…
We review in a unified way a recently proposed method to detect properties of unknown quantum channels and lower bounds to quantum capacities, without resorting to full quantum process tomography. The method is based on the preparation of a…