Optimal-speed unitary quantum time evolutions and propagation of light with maximal degree of coherence

TL;DR

This paper establishes a geometric connection between optimal quantum state evolutions and coherent light propagation, inspired by Grover's quantum search algorithm and classical wave interference, providing a new perspective on quantum and optical phenomena.

Contribution

It introduces a quantitative link between optimal-speed Hamiltonian evolutions and light coherence on the Poincaré sphere, rooted in the geometry of the Bloch sphere.

Findings

Link between quantum Hamiltonian evolution and light coherence

Geometric interpretation of interference phenomena

Insight into Grover's intuition through physical geometry

Abstract

It is recognized that Grover arrived at his original quantum search algorithm inspired by his comprehension of the interference of classical waves originating from an array of antennas. It is also known that quantum-mechanical characterization of electromagnetic radiation is isomorphic to the treatment of the orientation of a spin-1/2 particle. In this paper, motivated by Grover's original intuition and starting from this mathematical equivalence, we present a quantitative link between the geometry of time-independent optimal-speed Hamiltonian evolutions on the Bloch sphere and the geometry of intensity-preserving propagation of light with maximal degree of coherence on the Poincar\'e sphere. Finally, identifying interference as the fundamental physical ingredient underlying both physical phenomena, we propose that our work can provide in retrospect a quantitative geometric background underlying Grover's powerful intuition.