Related papers: Supermaps between channels of any type
Completely positive maps are useful in modeling the discrete evolution of quantum systems. Spectral properties of operators associated with such maps are relevant for determining the asymptotic dynamics of quantum systems subjected to…
Exceptional points (EPs) are special points in non-Hermitian systems where both eigenvalues and eigenvectors coalesce. In open quantum systems, these points are typically analyzed using effective non-Hermitian Hamiltonians or Liouvillian…
We establish necessary and sufficient conditions for the realization of mapping schemata as post-critically finite polynomials, or more generally, as post-critically finite polynomial maps from a finite union of copies of the complex…
In this article we provide necessary and sufficient conditions for a completely positive trace-preserving (CPT) map to be decomposable into a convex combination of unitary maps. Additionally, we set out to define a proper distance measure…
Quasiprobability representations are well-established tools in quantum information science, with applications ranging from the classical simulability of quantum computation to quantum process tomography, quantum error correction, and…
We describe the class (semigroup) of quantum channels mapping states with finite entropy into states with finite entropy. We show, in particular, that this class is naturally decomposed into three convex subclasses, two of them are closed…
We investigate the coherence of quantum channels and establish a resource theory for quantifying the coherence of quantum channels via Choi matrix. To this aim, we define the incoherent channels and incoherent superchannels. This theory…
Simulating quantum physical processes has been one of the major motivations for quantum information science. Quantum channels, which are completely positive and trace preserving processes, are the standard mathematical language to describe…
The problem of reconstructing a quantum channel from a sample of classical data is considered. When the total fidelity can be represented as a ratio of two quadratic forms (e.g., in the case of mapping a mixed state to a pure state,…
We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such as, e.g., cloning, discrimination,…
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…
Quasiregular maps are differentiable almost everywhere maps which are analogous to holomorphic maps in the plane for higher real dimensions. Introduced by Gutlyanskii et al, the infinitesimal space is a generalization of the notion of…
Pauli channels are fundamental in the context of quantum computing as they model the simplest kind of noise in quantum devices. We propose a quantum algorithm for simulating Pauli channels and extend it to encompass Pauli dynamical maps…
We analyze two ways to obtain distinguishability measures between quantum maps by employing the square root of the quantum Jensen-Shannon divergence, which forms a true distance in the space of density operators. The arising measures are…
Problems based on the structure of graphs -- for example finding cliques, independent sets, or colourings -- are of fundamental importance in classical complexity. Defining well-formulated decision problems for quantum graphs, which are an…
A special class of quantum channels, named subspace local (SL), are defined and investigated. The proposed definition of subspace locality of quantum channels is an attempt to answer the question of what kind of restriction should be put on…
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…
A quantum channel will have a Choi representation from which the complete positivity (CP) can be determined in a number of different ways. Every method relies on Choi's proof which relates CP to the positive semi-definiteness of a specially…
We present a complete characterization of diagonal unitary covariant (DU-covariant) superchannels, i.e. higher-order transformations transforming quantum channels into themselves. Necessary and sufficient conditions for complete positivity…
We consider quantum channels with one sender and two receivers, used in several different ways for the simultaneous transmission of independent messages. We begin by extending the technique of superposition coding to quantum channels with a…