Related papers: Covariance systems
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…
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
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.…
A characterization of qubit quantum channels is introduced. In analogy to what happens in the context of Bosonic channels we exploit the possibility of representing the states of the system in terms of characteristic function. The latter…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
Due to the exponential growth of the Hilbert space dimension with system size, the simulation of quantum many-body systems has remained a persistent challenge until today. Here, we review a relatively new class of variational states for the…
Bound and scattering state Schr\"odinger functions of nonrelativistic quantum mechanics as representation matrix elements of space and time are embedded into residual representations of spacetime as generalizations of Feynman propagators.…
The quasiprobability representation of quantum states addresses two main concerns, the identification of nonclassical features and the decomposition of the density operator. While the former aspect is a main focus of current research, the…
Characterization and categorization of quantum correlations are both fundamentally and practically important in quantum information science. Although quantum correlations such as non-separability, steerability, and non-locality can be…
We briefly review a perspective along which the Boltzmann-Gibbs statistical mechanics, the strongly chaotic dynamical systems, and the Schroedinger, Klein-Gordon and Dirac partial differential equations are seen as linear physics, and are…
I investigate the extent to which the description of quantum systems by Gibbs states can be justified purely on the basis of tomographic data, without recourse to theoretical concepts such as infinite ensembles, environments, information,…
We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or…
An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is…
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems and we introduce the notion of coefficient of quantum correlations. Our presentation stems from rigorous…
In this paper we propose the idea that there is a corresponding relation between quantum states and points of the complex projective space, given that the number of dimensions of the Hilbert space is finite. We check this idea through…
This work introduces a novel approach to quantum simulation by leveraging continuous-variable systems within a photonic hardware-inspired framework. The primary focus is on simulating static properties of the ground state of Hamiltonians…
The measurement processes that are traditionally described within the realm of non-relativistic quantum mechanics are transcribed into the covariant framework of Cartan's space, the four-valued representation space of the restricted…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
Weakly nonlinear energy transfer between normal modes of strongly resonant PDEs is captured by the corresponding effective resonant systems. In a previous article, we have constructed a large class of such resonant systems (with specific…