Related papers: Unified framework for generalized quantum statisti…
We provide an extended acount of the recent statistical mechanical theory of gauge invariance against operator shifting in quantum many-body systems (arXiv:2509.20494). The gauge transformation is enacted by a shifting superoperator that…
Usual quantum statistics is written in Fock space but it is not an algebraic theory. We show that at a deeper level it can be algebraically formalized defining the different statistics as (multi-mode) coherent states of the appropriate (but…
We show the possibility of describing fractional exclusion statistics (FES) as an occupancy process with global and \textit{local} exclusion constraints. More specifically, using combinatorial identities, we show that FES can be viewed as…
We show that (in contrast to a rather common opinion) QM is not a complete theory. This is a statistical approximation of classical statistical mechanics on the {\it infinite dimensional phase space.} Such an approximation is based on the…
Gibbs states are known to play a crucial role in the statistical description of a system with a large number of degrees of freedom. They are expected to be vital also in a quantum gravitational system with many underlying fundamental…
Graphical Models have various applications in science and engineering which include physics, bioinformatics, telecommunication and etc. Usage of graphical models needs complex computations in order to evaluation of marginal functions,so…
The use of imaginary numbers in modelling quantum mechanical systems encompasses the wave-like nature of quantum states. Here we introduce a resource theoretic framework for imaginarity, where the free states are taken to be those with…
A brief presentation of the basic concepts in quantum probability theory is given in comparison to the classical one. The notion of quantum white noise, its explicit representation in Fock space, and necessary results of noncommutative…
The connection between the intrinsic angular momentum (spin) of particles and the quantum statistics is established by considering the response of identical particles to a common background radiation field. For this purpose, the Hamiltonian…
Let $T=\mathbb R^d$. Let a function $Q:T^2\to\mathbb C$ satisfy $Q(s,t)=\bar{Q(t,s)}$ and $|Q(s,t)|=1$. A generalized statistics is described by creation operators $\partial_t^\dag$ and annihilation operators $\partial_t$, $t\in T$, which…
The work performed on or extracted from a non-autonomous quantum system described by means of a two-point projective-measurement approach takes the form of a stochastic variable. We show that the cumulant generating function of work can be…
A software product line models the variability of highly configurable systems. Complete exploration of all valid configurations (the configuration space) is infeasible as it grows exponentially with the number of features in the worst case.…
We introduce and study norms in the space of hermitian operators, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum…
Obtaining the expectation value of an observable on a quantum computer is a crucial step in the variational quantum algorithms. For complicated observables such as molecular electronic Hamiltonians, a common strategy is to present the…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
Canonical quantization relies on Cartesian, canonical, phase-space coordinates to promote to Hermitian operators, which also become the principal ingredients in the quantum Hamiltonian. While generally appropriate, this procedure can also…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
We analyse a n-dimensional Generalized Uncertainty Principle (GUP) quantization framework, characterized by a non-commutative nature of the configurational variables. First, we identify a set of states which are maximally localized only…
We describe the implications of permutation symmetry for the state space and dynamics of quantum mechanical systems of matrices of general size $N$. We solve the general 11- parameter permutation invariant quantum matrix harmonic oscillator…