Related papers: Generalizations of quantum statistics
Generalized quantum statistics (GQS) associated to a Lie algebra or Lie superalgebra extends the notion of para-Bose or para-Fermi statistics. Such GQS have been classified for all classical simple Lie algebras and basic classical Lie…
I discuss theories of violations of statistics, including intermediate statistics, parastatistics, parons, and quons. I emphasize quons, which allow small violations of statistics. I analyze the quon algebra and its representations,…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
A generalization of $A_r$ statistics is proposed and developed. The generalized $A_r$ quantum statistics is completely specified by a set of Jacobson generators satisfying a set of triple algebraic relations. Fock-Hilbert representations…
In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy and quantum relative entropy, as well as…
Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin-statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose-Fermi case…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
Generalized quantum measurements are an important extension of projective or von Neumann measurements, in that they can be used to describe any measurement that can be implemented on a quantum system. We describe how to realize two…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
Conservation of statistics requires that fermions be coupled to Grassmann external sources. Correspondingly, conservation of statistics requires that parabosons, parafermions and quons be coupled to external sources that are the appropriate…
The determination of a quantum observable from the first and second moments of its measurement outcome statistics is investigated. Operational conditions for the moments of a probability measure are given which suffice to determine the…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
Quantum matter in three spatial dimensions is observed to consist exclusively of bosons and fermions. Whether this empirical fact follows from basic consistency requirements of quantum theory itself or must be imposed as an additional…
A short review is given of how to apply the algebraic Heisenberg quantization scheme to a system of identical particles. For two particles in one dimension the approach leads to a generalization of the Bose and Fermi description which can…
We carry out a generalization of quantum group co-representations in order to encode in this structure those cases where non-commutativity between endomorphism matrix entries and quantum space coordinates happens.
General permutation invariant statistics in the second quantized approach are considered. Simple interpolations between dual statistics are constructed. Particularly, we present a new minimal interpolation between parabosons and…
A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised…
In a Generalised Probabilistic Theory (GPT) equipped additionally with some extra geometric structure we define the morphophoric measurements as those for which the measurement map sending states to distributions of the measurement results…
We generalize the quantum "pigeonhole paradox" to quantum paradoxes involving arbitrary types of particle relations, including orderings, functions and graphs.