Related papers: A probabilistic operator symbol framework for quan…
We elucidate physical aspects of path signatures by formulating randomised path developments within the framework of matrix models in quantum field theory. Using tools from physics, we introduce a new family of randomised path developments…
In the paper is discussed complete probabilistic description of quantum systems with application to multiqubit quantum computations. In simplest case it is a set of probabilities of transitions to some fixed set of states. The probabilities…
We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral…
We introduce a new mathematical framework for the probabilistic description of an experiment on a system of any type in terms of information representing this system initially. Based on the notions of an information state and a generalized…
Quantum coherence and distributed correlations among subparties are often considered as separate, although operationally linked to each other, properties of a quantum state. Here, we propose a measure able to quantify the contributions…
We present "Diagrams of States", a way to graphically represent and analyze how quantum information is elaborated during the execution of quantum circuits. This introductory tutorial illustrates the basics, providing useful examples of…
Requirements of a conjugate operator are emphasized, especially in its role in uncertainty relations.It is argued that in many contexts it is necessary to extend the Hilbert space in order to define a conjugate operator as in gauge…
It is shown that an operator can be defined in the abstract space of random matrices ensembles whose matrix elements statistical distribution simulates the behavior of the distribution found in real physical systems. It is found that the…
Inspired by the spin geometry theorem, two operators are defined which measure angles in the quantum theory of geometry. One operator assigns a discrete angle to every pair of surfaces passing through a single vertex of a spin network. This…
Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
To develop a unitary quantum theory with probabilistic description for pseudo- Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different…
Stochastic and bistochastic matrices providing positive maps for spin states (for qudits) are shown to form semigroups with dense intersection with the Lie groups $IGL(n, \mathbb{R})$ and $GL(n, \mathbb{R})$ respectively. The density matrix…
In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, Quantum state…
Two schemes for sharing an arbitrary two-qubit state based on entanglement swapping are proposed with Bell-state measurements and local unitary operations. One is based on the quantum channel with four Einstein-Podolsky-Rosen (EPR) pairs…
In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors…
We propose a probabilistic quantum protocol to realize a nonlinear transformation of qutrit states, which by iterative applications on ensembles can be used to distinguish two types of pure states. The protocol involves single-qutrit and…
Quantum Information is a new area of research which has been growing rapidly since last decade. This topic is very close to potential applications to the so called Quantum Computer. In our point of view it makes sense to develop a more…
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…