相关论文: Some properties of the potential-to-ground state m…

The energy gap is calculated for the ground state quantum computer circuit, which was recently proposed by Mizel et.al. When implementing a quantum algorithm by Hamiltonians containing only pairwise interaction, the inverse of energy gap…

New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They…

Structural and static properties of a classical two-dimensional (2D) system consisting of a finite number of charged particles which are laterally confined by a parabolic potential are investigated by Monte Carlo (MC) simulations and the…

Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot…

The geometrical arrangement of a set of quantum states can be completely characterized using relational information only. This information is encoded in the pairwise state overlaps, as well as in Bargmann invariants of higher degree written…

We investigate the relationship between the energy spectrum of a local Hamiltonian and the geometric properties of its ground state. By generalizing a standard framework from the analysis of Markov chains to arbitrary (non-stoquastic)…

We consider transformation maps on the space of states which are symmetries in the sense of Wigner. Due to the convex nature of the space of states, the set of these maps has a convex structure. We investigate the possibility of a complete…

In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum…

We investigate the effect of curvature on the behaviour of a quantum particle bound to move on a surface. For the Gaussian bump we derive and discuss the quantum potential which results in the appearance of a bound state for particles with…

The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…

We find the covariant deformed Heisenberg algebra and the Laplace-Beltrami operator on the extended $h$-deformed quantum plane and solve the Schr\"odinger equations explicitly for some physical systems on the quantum plane. In the…

We investigate bosonic Gaussian quantum states on an infinite cubic lattice in arbitrary spatial dimensions. We derive general properties of such states as ground states of quadratic Hamiltonians for both critical and non-critical cases.…

We derive a general framework that connects every positive map with a corresponding witness for partial separability in multipartite quantum systems. We show that many previous approaches were intimately connected to the witnesses derived…

Ground-state entanglement induces emergence of negative-energy-density regions in quantum systems by squeezing zero-point oscillation, keeping total energy of the systems nonnegative. By use of the negativity of quantum energy density,…

Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by…

I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…

We analyze the eigenstates of a two-dimensional lattice with additional harmonic confinement in the presence of an artificial magnetic field. While the softness of the confinement makes a distinction between bulk and edge states difficult,…

We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…

This paper treats a quantum network from a physical approach, explicitly finds the physical eigenstates and compares them to the quantum-graph description. The basic building block of a quantum network is an X-shaped potential well made by…

We investigate which nonlocal-interaction energies have a ground state (global minimizer). We consider this question over the space of probability measures and establish a sharp condition for the existence of ground states. We show that…