Related papers: Quantum reference frames for general symmetry grou…
We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms, in the framework of compact quantum group theory and…
In order to communicate information in a quantum network effectively, all network nodes should share a common reference frame. Here, we propose to study how well m nodes in a quantum network can establish a common reference frame from…
We consider a general symplectic transformation (also known as linear canonical transformation) of quantum-mechanical observables in a quantized version of a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q}…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
Non-invertible symmetries of a quantum field theory (QFT) are a natural generalization of unitary symmetries, but in which the product of operators does not satisfy a group multiplication law. We show that such symmetry operations on states…
In this paper we give a review of the most general approach to description of reference frames, the monad formalism. This approach is explicitly general covariant at each step, permitting to use abstract representation of tensor quantities;…
Newtonian mechanics has the concept of an absolute inertial rest frame. Special relativity eliminates the absolute rest frame but continues to require the absolute inertial frame. General relativity solves this for gravity by requiring…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
We develop a Heisenberg-picture \emph{kinematical} framework in which (i) time is treated as a quantum observable, admitting both a relational POVM construction for semibounded spectra and a fully self-adjoint realization on an enlarged…
In this work we use generalized deformed gauge groups for investigation of symmetry of general relativity (GR). GR is formulated in generalized reference frames, which are represented by (anholonomic in general case) affine frame fields.…
A universal formulation of uncertainty relations for quantum measurements is presented with additional focus on the representability of quantum observables by classical observables over a given state. Owing to the simplicity and operational…
We investigate the physics of quantum reference frames. Specifically, we study several simple scenarios involving a small number of quantum particles, whereby we promote one of these particles to the role of a quantum observer and ask what…
The Galilei group has been taken as the fundamental symmetry for 'nonrelativistic' physics, quantum or classical. Our fully group theoretical formulation approach to the quantum theory asks for some adjustments. We present a sketch of the…
The framework of internal quantum reference frames (QRFs) constitutes a universal toolset for dealing with symmetries in quantum theory and has led to new revelations in quantum gravity, gauge theories and foundational physics. Multiple…
Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If…
We review some of our recent results concerning the relationship between the Real-Space Renormalization Group method and Quantum Groups. We show this relation by applying real-space RG methods to study two quantum group invariant…
In a series of papers we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra ${\cal A}_{\Gamma}$ defined on a transformation…
Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as…
It is quite common to use the generalized probabilistic theories (GPTs) as generic models to reconstruct quantum theory from a few basic principles and to gain a better understanding of the probabilistic or information theoretic foundations…
Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…