# Quantum localized states in photonic flat-band lattices

## TL;DR

This paper explores quantum light localization in flat-band photonic lattices, constructing localized quantum states, analyzing their properties, and proposing an experimental setup for their generation, with implications for quantum communication.

## Contribution

It introduces a quantum framework for localized states in flat-band lattices, including their construction, properties, and potential for robust quantum information transmission.

## Key findings

- Quantum localized states are eigenstates with zero eigenvalue and defined photon number.
- Superpositions of these states can recover classical localization.
- States enable passive suppression of photon crosstalk and are robust against losses.

## Abstract

The localization of light in flat-band lattices has been recently proposed and experimentally demonstrated in several configurations, assuming a classical description of light. Here, we study the problem of light localization in the quantum regime. We focus on quasi one-dimensional and two-dimensional lattices which exhibit a perfect flat-band inside their linear spectrum. Localized quantum states are constructed as eigenstates of the interaction Hamiltonian with a vanishing eigenvalue and a well defined total photon number. These are superpositions of Fock states with probability amplitudes given by positive as well as negative square roots of multinomial coefficients. The classical picture can be recovered by considering poissonian superpositions of localized quantum states with different total photon number. We also study the separability properties of flat band quantum states and apply them to the transmission of information via multi-core fibers, where these states allow for the total passive suppression of photon crosstalk and exhibit robustness against photon losses. At the end, we propose a novel on-chip setup for the experimental preparation of localized quantum states of light for any number of photons.