# Duality and quantum state engineering in cavity arrays

## TL;DR

This paper explores a duality between two coupled cavities and an array of cavities, enabling controlled photon transfer and high-fidelity generation of entangled states without populating intermediate cavities.

## Contribution

It introduces a duality framework that allows precise control of photon transfer and entangled state generation in cavity arrays, advancing quantum state engineering techniques.

## Key findings

- Achieves perfect photon transfer between any two cavities.
- Establishes conditions for high-fidelity NOON state generation.
- Demonstrates duality as a tool for quantum state control.

## Abstract

A system of two coupled cavities with $N-1$ photons is shown to be dynamically equivalent to an array of $N$ coupled cavities containing one photon. Every transition in the two cavity system has a dual phenomenon in terms of photon transport in the cavity array. This duality is employed to arrive at the required coupling strengths and nonlinearities in the cavity array so that controlled photon transfer is possible between any two cavities. This transfer of photons between two of the cavities in the array is effected without populating the other cavities. The condition for perfect transport enables perfect state transfer between any two cavities in the array. Further, possibility of high fidelity generation of generalized NOON states in two coupled cavities, which are dual to the Bell states of the photon in the cavity array, is established.