Related papers: Generalizations of quantum statistics
Signal analysis is built upon various resolutions of the identity in signal vector spaces, e.g. Fourier, Gabor, wavelets, etc. Similar resolutions are used as quantizers of functions or distributions, paving the way to a time-frequency or…
The original definition of quantum discord of bipartite states was defined over projective measurements, in this paper we discuss some generalizations of it. These generalizations are defined over general measurements, rank-one general…
The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of…
Any method for estimating the ensemble average of arbitrary operator (observables or not, including the density matrix) relates the quantity of interest to a complete set of observables, i.e. a quorum}. This corresponds to an expansion on…
The problem of quantization of general relativity is considered in the framework of noncommutative differential geometry. Operator analogues for interval, scalar curvature, values of the Einstein tensor are proposed. Quantum measurements of…
Deep learning has seen substantial achievements, with numerical and theoretical evidence suggesting that singularities of statistical models are considered a contributing factor to its performance. From this remarkable success of classical…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination,…
Quantum mechanics broadly classifies the particles into two categories: $(1)$ fermions and $(2)$ bosons. Fermions are half-integer spin particles, obeying Pauli's exclusion principle and Fermi-Dirac statistics. Whereas bosons are integer…
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…
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…
Quantum systems invariant under particle exchange are either Bosons or Fermions, even though quantum theory in principle admits more general behavior under permutations. But why do we not observe such "paraparticles" in nature? The analysis…
The generalized quantal distribution functions are investigated concerning systems of non-interacting bosons and fermions. The formulae for the number of particles and energy are presented and applications to the Chandrasekhar limit of…
A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of…
We give a short overview over recent developments on quantum graphs and outline the connection between general quantum graphs and so-called quantum random walks.
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
These notes provide an introduction to standard topics on quantum computation and communication for those who already have a basic knowledge of quantum mechanics. The main target audience are professional physicists as well as advanced…
We continue the program started in cond-mat/9809384 and explain the statistics of the excitations for the generalizations of the paired states in the quantum Hall effect in terms of the parafermion statistics. We show that these excitations…
A possible alternative route to a quantum theory of gravity is presented. The usual path is to quantize the gravitational field in order to introduce the statistical structure characteristic of quantum mechanics. The procedure followed here…
These Lecture Notes provide an elementary introduction to the quantization of two-dimensional quantum gravity. Nothing beyond undergratuate physics and mathematic is required. Explicit formulas for the partition functions for universes with…