Related papers: Quantum objects in a sheaf framework
I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum…
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…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
We describe all the localization observables of a quantum particle in a one-dimensional box in terms of sequences of unit vectors in a Hilbert space. An alternative representation in terms of positive semidefinite complex matrices is…
In the quantum mechanics of collision problems we must consider scattering states of the system. For these states, the wave functions do not remain in Hilbert space, but they are expressible in terms of generalized functions of a Gel'fand…
We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in…
Candidate microstates of a spherically symmetric geometry are constructed in the group field theory formalism for quantum gravity, for models including both quantum geometric and scalar matter degrees of freedom. The latter are used as a…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…
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 work lays the foundations of the theory of changeable sets. In author opinion, this theory, in the process of it's development and improvement, can become one of the tools of solving the sixth Hilbert problem least for physics of…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…
Until recently, a quantum instrument was defined to be a completely positive operation-valued measure from the set of states on a Hilbert space to itself. In the last few years, this definition has been generalized to such measures between…
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of…
Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…
Finite frame quantization is a discrete version of the coherent state quantization. In the case of a quantum system with finite-dimensional Hilbert space, the finite frame quantization allows us to associate a linear operator to each…
Phase is a basic ingredient for quantum states since quantum mechanics uses complex numbers to describe quantum states. In this letter, we introduce a rigorous framework to quantify the phase of quantum states. To do so, we regard phase as…
The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…