Related papers: Relations Between Quantum Maps and Quantum States

Diagrammatic representation and manipulation of tensor networks has proven to be a useful tool in mathematics, physics, and computer science. Here we present several important and mostly well-known theorems regarding the dualities between…

Assuming that quantum states, including pure states, represent subjective degrees of belief rather than objective properties of systems, the question of what other elements of the quantum formalism must also be taken as subjective is…

In quantum information theory it is generally accepted that quantum mutual information is an information-theoretic measure of total correlations of a bipartite quantum state. We argue that there exist quantum states for which quantum mutual…

A quantum state represents neither properties of a physical system nor anyone's knowledge of its properties. The important question is not what quantum states represent but how they are used---as informational bridges. Knowing about some…

A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…

Generalized measurement schemes on one part of bipartite states, which would leave the set of all separable states insensitive are explored here to understand quantumness of correlations in a more general perspecitve. This is done by…

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…

A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple…

We investigate the extent to which we can establish whether or not two quantum systems have been prepared in the same state. We investigate the possibility of universal unambiguous state comparison. We show that it is impossible to…

In quantum operations, probabilities characterise both the degree of the success of a state transformation and, as density operator eigenvalues, the degree of mixedness of the final state. We give a unified treatment of pure-to-pure state…

The subject of this thesis are various properties of quantum states that make them "non-classical" and their behaviour under unitary operations. In chapter 2 some basic concepts of quantum mechanics and quantum information are reviewed. In…

We outline a new approach to the characterization as well as to the classification of positive maps. This approach is based on the facial structures of the set of states and of the cone of positive maps. In particular, the equivalence…

We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all $N$ systems are in the same state. Alternatively, one may ask whether or not the states…

Models that provide experimentally testable violations of ordinary Quantum Mechanics have been recently proposed. These models are based on non-unitary time evolutions of density matrices that are generated by linear positive maps. We…

Linear maps of matrices describing evolution of density matrices for a quantum system initially entangled with another are identified and found to be not always completely positive. They can even map a positive matrix to a matrix that is…

We investigate completely positive maps for an open system interacting with its environment. The families of the initial states for which the reduced dynamics can be described by a completely positive map are identified within the framework…

The definition of the conditional probability is very important in the theory of the probability. This definition is based on the fact, that random events can be simultaneously measurable. This paper deal with the problem of conditioning…

In this paper, we examined the connection between quantum systems' indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in…

Quantum probabilities are defined for several important physical cases characterizing measurements with multimode quantum systems. These are the probabilities for operationally testable measurements, for operationally uncertain…

Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for…