Bending The Heisenberg Uncertainty Principle

TL;DR

This paper explores the possibility of surpassing traditional measurement limits set by the Heisenberg Uncertainty Principle through classical analogs like sub-Fourier sensitivity, demonstrated with compass states.

Contribution

It introduces a step-by-step illustration of sub-Fourier sensitivity in quantum states, challenging conventional interpretations of the uncertainty principle.

Findings

Demonstrates sub-Fourier sensitivity in compass states

Shows measurement accuracies can surpass traditional uncertainty bounds

Provides a classical analog to quantum measurement limits

Abstract

The celebrated Heisenberg Uncertainty Principle \Delta x \Delta p\ge \hbar/2 can allow measurement accuracies less than \Delta x or \Delta p. Classical analog of this is known as sub-Fourier sensitivity. We illustrate this phenomenon in a step by step process using the example of compass state, as suggested by Zurek.