Related papers: Comparison of quantum statistical models: equivale…
We describe society as a nonequilibrium probabilistic system: N individuals occupy W resource states in it and produce entropy S over definite time periods. Resulting thermodynamics is however unusual because a second entropy, H, measures a…
It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such…
The classical parametric and semiparametric Bernstein -- von Mises (BvM) results are reconsidered in a non-classical setup allowing finite samples and model misspecification. In the case of a finite dimensional nuisance parameter we obtain…
In a smooth semiparametric model, the marginal posterior distribution of the finite dimensional parameter of interest is expected to be asymptotically equivalent to the sampling distribution of frequentist's efficient estimators. This is…
Blind Source Separation (BSS) is an active domain of Classical Information Processing. The development of Quantum Information Processing has made possible the appearance of Blind Quantum Source Separation (BQSS). This article discusses some…
Identical quantum particles exhibit only two types of statistics: bosonic and fermionic. Theoretically, this restriction is commonly established through the symmetrization postulate or (anti)commutation constraints imposed on the algebra of…
Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac)…
Let H and K be Hilbert spaces and T be a coarse-graining from B(H) to B(K). Assume that density matrices D_1 and D_2 acting on H are given. In the paper the consequences of the existence of a coarse-graining S from B(K) to B(H) satisfying…
A statistical experiment on a von Neumann algebra is a parametrized family of normal states on the algebra. This paper introduces the concept of minimal sufficiency for statistical experiments in such operator algebraic situations. We…
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
Many inference problems, notably the stochastic block model (SBM) that generates a random graph with a hidden community structure, undergo phase transitions as a function of the signal-to-noise ratio, and can exhibit hard phases in which…
A conjecture due to Bohigas, Giannoni and Schmit (BGS), stating that the energy level correlations of quantum chaotic systems generically obey the laws of random matrix theory, is given a precise formulation for quantized symplectic maps.…
Continuous-variable bosonic systems stand as prominent candidates for implementing quantum computational tasks. While various necessary criteria have been established to assess their resourcefulness, sufficient conditions have remained…
We show that (1) the violation of the Ekert 91 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 92 (BBM) inequality is, also, a sufficient…
Consider $D$ random systems that are modeled by independent $N\times N$ complex Hermitian Wigner matrices. Suppose they are lying on a circle and the neighboring systems interact with each other through a deterministic matrix $A$. We prove…
The crucial feature of a memoryless stochastic process is that any information about its state can only decrease as the system evolves. Here we show that such a decrease of information is equivalent to the underlying stochastic evolution…
It is a key issue to characterize the model of standard quantum theory out of general models by an operational condition. The framework of General Probabilistic Theories (GPTs) is a new information theoretical approach to single out…
Logarithmic score and information divergence appear in both information theory, statistics, statistical mechanics, and portfolio theory. We demonstrate that all these topics involve some kind of optimization that leads directly to the use…
According to a recent no-go theorem (M. Pusey, J. Barrett and T. Rudolph, Nature Physics 8, 475 (2012)), models in which quantum states correspond to probability distributions over the values of some underlying physical variables must have…