Related papers: Probability Distributions and Hilbert Spaces: Quan…
When applied to different input states, an imperfect quantum operation yields output states with varying fidelities, defined as the absolute square of their overlap with the desired states. We present an expression for the distribution of…
We show that some N-particle quantum systems are holistic, such that the system is deterministic, whereas its parts are random. The total correlation is not sufficient to determine the probability distribution, showing a need for extra…
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
This paper explores the generalization of the concept of a "probability current", familiar from wave-function quantum mechanics, to quantum systems with finite-dimensional Hilbert spaces. The generalized definition applies both to isolated…
This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…
The restrictions that nature places on the distribution of correlations in a multipartite quantum system play fundamental roles in the evolution of such systems, and yield vital insights into the design of protocols for the quantum control…
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…
This Chapter develops a realist information-theoretic interpretation of the nonclassical features of quantum probabilities. On this view, what is fundamental in the transition from classical to quantum physics is the recognition that…
The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
We present a quantum-like (QL) model in that contexts (complexes of e.g. mental, social, biological, economic or even political conditions) are represented by complex probability amplitudes. This approach gives the possibility to apply the…
This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…
Classical probability theory is based on assumptions which are often violated in practice. Therefore quantum probability is a proposed alternative not only in quantum physics, but also in other sciences. However, so far it mostly criticizes…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
Integrability is a cornerstone of classical mechanics, where it has a precise meaning. Extending this notion to quantum systems, however, remains subtle and unresolved. In particular, deciding whether a quantum Hamiltonian - viewed simply…
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…
In this paper we introduce the concept of Hamiltonian system in the canonical and Poisson settings. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and quantum group…