# Generating double NOON states of photons in circuit QED

## TL;DR

This paper proposes a method to generate 'double NOON' entangled photon states in circuit QED using two superconducting flux qutrits and five cavities, requiring fewer steps and achieving high fidelity for N up to 10.

## Contribution

The authors introduce a novel scheme for creating double NOON states with fewer operational steps and high fidelity, advancing quantum entanglement generation in circuit QED.

## Key findings

- Double NOON states can be generated with N+2 steps.
- High fidelity is achievable for N up to 10.
- The method outperforms traditional NOON state schemes in efficiency.

## Abstract

To generate a NOON state with a large photon number $N$, the number of operational steps could be large and the fidelity will decrease rapidly with $N$. Here we propose a method to generate a new type of quantum entangled states, $(|NN00\rangle+|00NN\rangle)/\sqrt{2}$ called "double NOON" states, with a setup of two superconducting flux qutrits and five circuit cavities. This scheme operates essentially by employing a two-photon process, i.e., two photons are simultaneously and separately emitted into two cavities when each coupler qutrit is initially in a higher-energy excited state. As a consequence, the "double" NOON state creation needs only $N$+2 operational steps. One application of double NOON states is to get a phase error of $1/(2N)$ in phase measurement. In comparison, to achieve the same error, a normal NOON state of the form $(|2N,0\rangle+|0,2N\rangle)/\sqrt{2}$ is needed, which requires at least $2N$ operational steps to prepare by using the existing schemes. Our numerical simulation demonstrates that high-fidelity generation of the double NOON states with $N\leq 10$ even for the imperfect devices is feasible with the present circuit QED technique.