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Compressible models extend the domain of simulable systems in quantum computers, but little is known about their precise limits of applicability. Using the theory of compressible matchgate circuits, we identify a class of quadratic…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
In order to characterize quantum states within the context of information geometry, we propose a generalization of the Gaussian model, which we called the Hermite-Gaussian model. We obtain the Fisher-Rao metric and the scalar curvature for…
In this second paper on loop quantization of Gowdy model, we introduce the kinematical Hilbert space on which appropriate holonomies and fluxes are well represented. The quantization of the volume operator and the Gauss constraint is…
The interaction of classical gravitational waves (GW) with matter is studied within a quantum mechanical framework. The classical equations of motion in the long wave-length limit is quantized and a Schroedinger equation for the interaction…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
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…
We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…
Detecting the structure of spacetime with quantum technologies has always been one of the frontier topics of relativistic quantum information. Here, we analytically study the generation and redistribution of Gaussian entanglement of the…
Quantum optical Gaussian states are a type of important robust quantum states which are manipulatable by the existing technologies. So far, most of the important quantum information experiments are done with such states, including bright…
We apply a quantum version of dimensional reduction to Gaussian coherent states in Bargmann space to obtain squeezed states on complex projective spaces. This leads to a definition of a family of squeezed spin states with excellent…
The construction of oscillator-like systems connected with the given set of orthogonal polynomials and coherent states for such systems developed by authors is extended to the case of the systems with finite-dimensional state space. As…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
The problems which arise for a relativistic quantum mechanics are reviewed and critically examined in connection with the foundations of quantum field theory. The conflict between the quantum mechanical Hilbert space structure, the locality…
Extending the phase-space description of the Weyl-Wigner quantum mechanics to a subset of non-linear Hamiltonians in position and momentum, gaussian functions are identified as the quantum ground state. Once a Hamiltonian, $H^{W}(q,\,p)$,…
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
The quantum Zakharov system is described in terms of a Lagrangian formalism. A time-dependent Gaussian trial function approach for the envelope electric field and the low-frequency part of the density fluctuation leads to a coupled,…
Review of tomographic probability representation of quantum states is presented both for oscillator systems with continious variables and spin--systems with discrete variables. New entropic--information inequalities are obtained for…