# Nearly maximal violation of the Mermin-Klyshko inequality with multimode entangled coherent states

## TL;DR

This paper demonstrates that multimode entangled coherent states can nearly maximally violate the Mermin-Klyshko inequality with low average quantum numbers, and the violation grows exponentially with the number of modes, highlighting strong quantum correlations.

## Contribution

It shows that rotated quantum-number parity operators enable near-maximal Mermin-Klyshko inequality violations in multimode entangled states with minimal quantum number size.

## Key findings

- Violation approaches the maximum even with average quantum number of 1 per mode.
- Violation exponentially increases with the number of entangled modes.
- Rotated parity correlations differ significantly from displaced parity correlations.

## Abstract

Entangled coherent states for multiple bosonic modes, also referred to as multimode cat states, not only are of fundamental interest, but also have practical applications. The nonclassical correlation among these modes is well characterized by the violation of the Mermin-Klyshko inequality. We here study Mermin-Klyshko inequality violations for such multi-mode entangled states with rotated quantum-number parity operators. Our results show that the Mermin-Klyshko signal obtained with these operators can approach the maximal value even when the average quantum number in each mode is only 1, and the inequality violation exponentially increases with the number of entangled modes. The correlations among the rotated parities of the entangled bosonic modes are in distinct contrast with those among the displaced parities, with which a nearly maximal Mermin-Klyshko inequality violation requires the size of the cat state to be increased by about 15 times.