Related papers: Geometric derivation of quantum uncertainty
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…
Decoherence may not solve all of the measurement problems of quantum mechanics. It is proposed that a solution to these problems may be to allow that superpositions describe physically real systems in the following sense. Each quantum…
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…
The standard uncertainty relations (UR) in quantum mechanics are typically used for unbounded operators (like the canonical pair). This implies the need for the control of the domain problems. On the other hand, the use of (possibly…
We study Heisenberg's uncertainty relation relative to a quantum reference frame (QRF). We introduce the QRF as a covariant phase-space observable, show that when described relative to it, position and momentum appear compatible, and derive…
Symmetries are a central concept in our understanding of physics. In quantum theories, a quantum reference frame (QRF) can be used to distinguish between observables related by a symmetry. The framework of operational QRFs provides a means…
The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…
We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, the quantum universe appears two-dimensional…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Quantum coherence is an important quantum resource and it is intimately related to various research fields. The geometric coherence is a coherence measure both operationally and geometrically. We study the trade-off relation of geometric…
The concept of quantum coherence and its possible use as a resource are currently the subject of active researches. Uncertainty and complementarity relations for quantum coherence allow one to study its changes with respect to other…
Since Bell's theorem we know that quantum mechanics is incompatible with local hidden-variable models, the phenomenon known as quantum nonlocality. However, despite steady progress over the years, precise characterization of the set of…
Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased…
Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet…
We construct a space of quantum states and an algebra of quantum observables, over the set of all metrics of arbitrary but fixed signature, defined on a manifold. The construction is diffeomorphism invariant, and unique up to natural…
To unify general relativity and quantum theory is hard in part because they are formulated in two very different mathematical languages, differential geometry and functional analysis. A natural candidate for bridging this language gap, at…
In certain circumstances, the uncertainty, $\Delta S [\phi]$, of a quantum observable, $S$, can be bounded from below by a finite overall constant $\Delta S>0$, \emph{i.e.}, $\Delta S [\phi] \geq \Delta S$, for all physical states $\phi$.…
This article contains a survey of the geometric approach to quantum correlations. We focus mainly on the geometric measures of quantum correlations based on the Bures and quantum Hellinger distances.
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
Although a precise description of microscopic physical problems requires a full quantum mechanical treatment, physical quantities are generally discussed in terms of classical variables. One exception is quantum entanglement which…