Related papers: Extremality conditions for generalized channels
We derive an extremal equation for optimal completely-positive map which most closely approximates a given transformation between pure quantum states. Moreover, we also obtain an upper bound on the maximal mean fidelity that can be attained…
We develop a device-independent framework for testing quantum channels. That is, we falsify a hypothesis about a quantum channel based only on an observed set of input-output correlations. Formally, the problem consists of characterizing…
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…
With the control of ever more complex quantum systems becoming a reality, new scenarios are emerging where generalizations of the most foundational aspects of statistical quantum mechanics are imperative. In such experimental scenarios the…
We characterize the completely positive trace-preserving maps on qutrits (qutrit channels) according to their covariance and symmetry properties. Both discrete and continuous groups are considered. It is shown how each symmetry group…
The paper is devoted to systematic study of the $\chi$-capacity (underlying the classical capacity) of infinite dimensional quantum channels. An essential feature of this case is the natural appearance of the input constraints and infinite,…
Convex sets of quantum states and processes play a central role in quantum theory and quantum information. Many important examples of convex sets in quantum theory are spectrahedra, that is, sets of positive operators subject to affine…
Quantum channels describe the most general dynamics of open quantum systems. A quantum channel, as a linear map on vectorized quantum states, can be represented by a single matrix, whose spectrum is called the channel spectrum. Here we…
Calculations for open quantum systems are performed usually by taking into account their embedding into one common environment, which is mostly the common continuum of scattering wavefunctions. Realistic quantum systems are coupled however…
For a quantum channel (completely positive, trace-preserving map), we prove a generalization to the infinite dimensional case of a result by Baumgartner and Narnhofer. This result is, in a probabilistic language, a decomposition of a…
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…
Constructing all extreme instances of the set of completely positive trace-preserving (CPTP) maps, i.e., quantum channels, is a challenging valuable open problem in quantum information theory. Here we introduce a systematic approach that…
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…
Evaluating the channel capacity is one of many key problems in information theory. In this work we derive rather-mild sufficient conditions under which the capacity is finite and achievable. These conditions are derived for generic,…
The set of Entanglement Saving (ES) quantum channels is introduced and characterized. These are completely positive, trace preserving transformations which when acting locally on a bipartite quantum system initially prepared into a…
We characterize the extremal points of the convex set of quantum measurements that are covariant under a finite-dimensional projective representation of a compact group, with action of the group on the measurement probability space which is…
Necessary and sufficient conditions for approximation of a general channel by a general source are proved. For the special case in which the channel input is deterministic, which corresponds to source simulation, we prove a stronger…
We consider a nontrivial class of infinite dimensional quantum channels characterized by finiteness of the Holevo capacity. Some general properties of channels of this class are described. In particular, a special sufficient condition of…
We consider the problem of discriminating qubit states that are sent over a quantum channel and derive a necessary and sufficient condition for an optimal measurement to be preserved by the channel. We apply the result to the…
We define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite…