Related papers: On the notion of quantum copulas
Like a silver thread, quantum entanglement [1] runs through the foundations and breakthrough applications of quantum information theory. It cannot arise from local operations and classical communication (LOCC) and therefore represents a…
This paper describes an algorithmic system called SQT for the computer simulation of a wide class of quantum experiments on entangled particles. SQT maintains a hidden internal state for each particle and it provides an initialization…
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…
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…
Perhaps the quantum state represents information about reality, and not reality directly. Wave function collapse is then possibly no more mysterious than a Bayesian update of a probability distribution given new data. We consider models for…
In this paper we consider the notion of quantum entanglement from the perspective of the logos categorical approach [26, 27]. Firstly, we will argue that the widespread distinctions, on the one hand, between pure states and mixed states,…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based…
In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a…
The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear…
The most irreducible way to represent information is a sequence of two symbols. In this paper, we construct quantum states using this basic building block. Specifically, we show that the probabilities that arise in quantum theory can be…
Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number of a quantum channel. It enables one to define classes of quantum channels which partially break quantum entanglement.…
A new class of copulas based on order statistics was introduced by Baker (2008). Here, further properties of the bivariate and multivariate copulas are described, such as that of likelihood ratio dominance (LRD), and further bivariate…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
Since the quantum field theory treats a system of particles, there must be a distribution which is associated with the system of particles. It means that a meaningful quantity is adjoined in the system of particles. It seems that these…
Nonseparability - multipartite states that cannot be factorized - is one of the most striking features of quantum mechanics, as it gives rise to entanglement and non-causal correlations. In quantum computing, it also contributes directly to…
The cluster state model for quantum computation [Phys. Rev. Lett. 86, 5188] outlines a scheme that allows one to use measurement on a large set of entangled quantum systems in what is known as a cluster state to undertake quantum…
According to the stochastic-quantum correspondence, a quantum system can be understood as a stochastic process unfolding in an old-fashioned configuration space based on ordinary notions of probability and `indivisible' stochastic laws,…
In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy and quantum relative entropy, as well as…