Related papers: A geometric formulation of uncertainty principle
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by…
The uncertainty relation and the probability interpretation of quantum mechanics are intrinsically connected, as is evidenced by the evaluation of standard deviations. It is thus natural to ask if one can associate a very small uncertainty…
According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily…
We demonstrate that for an arbitrary number of identical particles, each defined on a Hilbert-space of arbitrary dimension, there exists a whole ladder of relations of complementarity between local, and every conceivable kind of joint (or…
The Schrodinger equation is incomplete, inherently unable to explain the collapse of the wavefunction caused by measurement; a fundamental issue known as the quantum measurement problem. Quantum mechanics is generally constrained by the…
The interplay between quantum geometry and electron correlation has emerged as a compelling paradigm in quantum many-body physics. Recent studies have highlighted the diagnostic utility of quantum geometry in identifying magnetic…
A common knowledge suggests that trajectories of particles in quantum mechanics always have quantum uncertainties. These quantum uncertainties set by the Heisenberg uncertainty principle limit precision of measurements of fields and forces,…
We study geometrical aspects of entanglement, with the Hilbert--Schmidt norm defining the metric on the set of density matrices. We focus first on the simplest case of two two-level systems and show that a ``relativistic'' formulation leads…
Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is…
We propose a new approach to the problem of defining the degree of entanglement between two particles in a pure state with Hilbert spaces of arbitrary finite dimensions. The central idea is that entanglement gives rise to correlations…
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…
We analyze mean fidelity between random density matrices of size N, generated with respect to various probability measures in the space of mixed quantum states: Hilbert-Schmidt measure, Bures (statistical) measure, the measures induced by…
Quantum physics constrains the accuracy of joint measurements of incompatible observables. Here we test tight measurement-uncertainty relations using single photons. We implement two independent, idealized uncertainty-estimation methods,…
Since the dawn of quantum theory, coherence was attributed as a key to understand the weirdness of fundamental concepts like the wave-particle duality and the Stern-Gerlach experiment. Recently, based on a resource theory approach, the…
We revisit, in the framework of Mach-Zehnder interferometry, the connection between the complementarity and uncertainty principles of quantum mechanics. Specifically, we show that, for a pair of suitably chosen observables, the trade-off…
In quantum field theory, virtual particles are carriers of relativistic wave fields, participate in vacuum fluctuations, and are a consequence of the implementation of the quantum uncertainty mechanism. Virtual particles, playing a…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
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…
We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…