'Complementarity' in paraxial and non-paraxial optical beams

TL;DR

This paper establishes a mathematical link between optical beam types and quantum systems, deriving a complementarity relation involving coherence, predictability, and entropy, with implications for quantum manipulation.

Contribution

It introduces a novel complementarity relation connecting coherence, predictability, and entropy in optical beams and quantum systems, enhancing understanding of their geometric and entanglement properties.

Findings

Linear entropy saturates the complementarity relation for mixed states.

For pure states, the relation reduces to a triality among coherence, predictability, and entanglement.

The relations provide insights into quantum property manipulation.

Abstract

Establishing the correspondence of two dimensional paraxial and three dimensional non-paraxial optical beams with the qubit and qutrit systems respectively, we derive a complementary relation between Hilbert-Schmidt coherence, generalized predictability and linear entropy. The linear entropy, a measure of mixedness is shown to saturate the complementarity relation for mixed bi-partite states. For pure two qubit and qutrit systems, it quantifies the global entanglement and reduces the complementarity relation to the triality relation between coherence, predictability and entanglement. We analyze these relations in wedge-product formalism in order to investigate the innate geometry of the complex vector space. The derived complementary relations offer insights into our ability to manipulate and utilize quantum properties for practical advancements.