Related papers: On the notion of quantum copulas
We introduce a quantum generalisation of the notion of coupling in probability theory. Several interesting examples and basic properties of quantum couplings are presented. In particular, we prove a quantum extension of Strassen theorem for…
We present a general description of separable states in Quantum Mechanics. In particular, our result gives an easy proof that inseparabitity (or entanglement) is a pure quantum (noncommutative) notion. This implies that distinction between…
Copulas are essential tools in statistics and probability theory, enabling the study of the dependence structure between random variables independently of their marginal distributions. Among the various types of copulas, Ratio-Type Copulas…
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…
Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…
Quantum information theory is a rapidly growing area of math and physics that combines two independent theories, quantum mechanics and information theory. Quantum entanglement is a concept that was first proposed in the EPR paradox. In…
We explore a particular way of reformulating quantum theory in classical terms, starting with phase space rather than Hilbert space, and with actual probability distributions rather than quasiprobabilities. The classical picture we start…
The collapse of a quantum state can be understood as a mathematical way to construct a joint probability density even for operators that do not commute. We can formalize that construction as a non-commutative, non-associative collapse…
To handle the ubiquitous problem of "dependence learning," copulas are quickly becoming a pervasive tool across a wide range of data-driven disciplines encompassing neuroscience, finance, econometrics, genomics, social science, machine…
We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by…
A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
This paper presents an introduction to the stochastic concepts of \emph{coupling} and \emph{copula}. Coupling means the construction of a joint distribution of two or more random variables that need not be defined on one and the same…
This article is a short introduction to and review of the cluster-state model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of single-qubit measurements applied to a fixed quantum…
The propagation of general electronic quantum states provides information of the interaction of molecular systems with external driving fields. These can also offer understandings regarding non-adiabatic quantum phenomena. Well established…