Related papers: On the Choi-Jamiolkowski Correspondence in Infinit…
In the space of quantum channels, we establish the geometry that allows us to make statistical predictions about relative volumes of entanglement breaking channels among all the Gaussian quantum channels. The underlying metric is…
The coding theorem for the entanglement-assisted communication via infinite-dimensional quantum channel with linear constraint is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and…
In this paper we give a general integral representation for separable states in the tensor product of infinite dimensional Hilbert spaces and provide the first example of separable states that are not countably decomposable. We also prove…
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…
Quantum entanglement can be studied through the theory of completely positive maps in a number of ways, including by making use of the Choi-Jamilkowski isomorphism, which identifies separable states with entanglement breaking quantum…
Sender and receiver can control noisy channels by means of the resources they own, that is local operations, potentially correlated using classical communication, and entangled pairs shared between them. Using the Choi-Jamiolkowski…
We give a representation for entanglement-breaking channels in separable Hilbert space that generalizes the "Kraus decomposition with rank one operators" and use it to describe the complementary channels. We also give necessary and…
Modern applications in quantum computation and quantum communication require the precise characterization of quantum states and quantum channels. In practice, this means that one has to determine the quantum capacity of a physical system in…
In the present work, we introduce and study the concepts of state and quantum channel on spaces equipped with an indefinite metric. Exclusively, we will limit our analysis to the matricial framework. As it will be confirmed below, from our…
We give a sufficient condition that an operator sum representation of a separable quantum channel in terms of product operators is the unique product representation for that channel, and then provide examples of such channels for any number…
In this article, I use an operational formulation of the Choi-Jamio\l{}kowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of…
The complete positivity vs positivity correspondence in the Choi-Jamio{\l}kowski-Kraus-Sudarshan quantum channel-state isomorphism depends on the choice of basis. Instead of the "canonical" basis, if we use, e.g., the Pauli spin matrices…
We address various aspects of a widely used tool in quantum information theory: the Choi-Jamiolkowski isomorphism [A. Jamiolkowski, Rep. Math. Phys., 3, 275 (1972)]. We review different versions of the isomorphism, their properties and…
A definition of the Schmidt number of a state of an infinite dimensional bipartite quantum system is given and properties of the corresponding family of Schmidt classes are considered. The existence of states with a given Schmidt number…
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…
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,…
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…
We show that entangling capacities based on the Jamiolkowski isomorphism may be used to place lower bounds on the communication capacities of arbitrary bipartite unitaries. Therefore, for these definitions, the relations which have been…
We propose a definition of infinite dimensional Choi-Jamiolkowski state associated with a completely positive trace preserving map. We introduce the notion of Theta-KMS adjoint of a quantum Markov semigroup, which is identified with the…
By establishing CHSH operators and CHSH-type inequalities, we show that any entangled pure state in infinite-dimensional systems is entangled in a $2\otimes2$ subspace. We find that, for infinite-dimensional systems, the corresponding…