Related papers: Quantum channels, complex Stiefel manifolds, and o…
In this work we present a general mathematical framework to deal with Quantum Networks, i.e. networks resulting from the interconnection of elementary quantum circuits. The cornerstone of our approach is a generalization of the Choi…
Supermaps between quantum channels (completely positive trace-preserving (CPTP) maps of matrix algebras) were introduced in [Chiribella et al., EPL 83(3) (2008)]. In this work we generalise to supermaps between channels of any type; by…
A pair of quantum channels are said to be incompatible if they cannot be realized as marginals of a single channel. This paper addresses the general structure of the incompatibility of completely positive channels with a fixed quantum input…
We argue that notions in quantum theory should have universal properties in the sense of category theory. We consider the completely positive trace preserving (CPTP) maps, the basic notion of quantum channel. Physically, quantum channels…
Quantum coherence is a fundamental aspect of quantum physics and plays a central role in quantum information science. This essential property of the quantum states could be fragile under the influence of the quantum operations. The extent…
We study the problem of approximating a quantum channel by one with as few Kraus operators as possible (in the sense that, for any input state, the output states of the two channels should be close to one another). Our main result is that…
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,…
Many theoretical problems in quantum technology can be formulated and addressed as constrained optimization problems. The most common quantum mechanical constraints such as, e.g., orthogonality of isometric and unitary matrices, CPTP…
Quantum channels can represent dynamic resources, which are indispensable elements in many physical scenarios. To describe certain facets of nonclassicality of the channels, it is necessary to quantify their properties. In the framework of…
Tensor networks representations of many-body quantum systems can be described in terms of quantum channels. We focus on channels associated with the Multi-scale Entanglement Renormalization Ansatz (MERA) tensor network that has been…
We consider properties of quantum channels with use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The…
In this paper a notion of entropy transmission of quantum channels is introduced as a natural extension of Ohya's entropy. Here by quantum channel is meant unital completely positive mappings (ucp) of $B(H)$ into itself, where $H$ is an…
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…
We formulate the notion of quantum channels in the framework of quantum tomography and address there the issue of whether such maps can be regarded as classical stochastic maps. In particular kernels of maps acting on probability…
The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective…
The fragile nature of quantum information makes it practically impossible to completely isolate a quantum state from noise under quantum channel transmissions. Quantum networks are complex systems formed by the interconnection of quantum…
Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…
A convex optimization based method is proposed for quantum process tomography, in the case of known channel model structure, but unknown channel parameters. The main idea is to select an affine parametrization of the Choi matrix as a set of…
A generalization of the Choi-Jamiolkowski isomorphism for completely positive maps between operator algebras is introduced. Particular emphasis is placed on the case of normal unital completely positive maps defined between von Neumann…
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state. The second one is based on the relative entropy…