# Quantum correlations and complementarity of vectorial light fields

## TL;DR

This paper investigates quantum correlations in vector light fields, revealing a fundamental triality identity that links wave-particle duality and establishes a general quantum complementarity relation across multiple slits and states.

## Contribution

It introduces a novel framework connecting field coherence matrices with photon density matrices, transforming duality inequalities into equalities and uncovering fundamental quantum interference physics.

## Key findings

- Derived a direct link between field coherence and photon density matrices.
- Revealed a hidden information-theoretic contribution to wave-particle duality.
- Established a universal quantum complementarity relation for vector-light fields.

## Abstract

We explore quantum correlations of general vector-light fields in multislit interference and show that the $n$th-order field-coherence matrix is directly linked with the reduced $n$-photon density matrix. The connection is utilized to examine photon wave-particle duality in the double-slit configuration, revealing that there is a hidden information-theoretic contribution that complements the standard inequality associated with such duality by transforming it into a strict equality, a triality identity. We also establish a general quantum complementarity relation among the field correlations and the particle correlations which holds for any number of slits, correlation orders, and vector-light states. The framework that we advance hence uncovers fundamental physics about quantum interference.