An Entropic Uncertainty Principle for Quantum Measurements

TL;DR

This paper generalizes the entropic uncertainty principle to include arbitrary quantum measurements, extending previous results beyond non-degenerate observables to encompass degenerate measurements and single measurement cases.

Contribution

It introduces a new entropic uncertainty relation applicable to all quantum measurements, including degenerate and single measurements, broadening the scope of uncertainty principles.

Findings

Generalized entropic uncertainty principle for arbitrary measurements

Includes cases of degenerate observables and single measurements

Provides a unified framework for measurement uncertainty

Abstract

The entropic uncertainty principle as outlined by Maassen and Uffink for a pair of non-degenerate observables in a finite level qusystem is generalized here to the case of a pair of arbitrary quantum measurements. In particular, our result includes not only the case of projectivmeasurements (or equivalently, observables) exhibiting degeneracy but also an uncertainty principle for a single measurement.