# Optical Zeno Gate: Bounds for Fault Tolerant Operation

## TL;DR

This paper explores enhancing the fidelity of the optical Zeno gate using measurement-based quantum processing and quantum teleportation, achieving near-unit fidelity with moderate success probability under realistic loss conditions.

## Contribution

It introduces a method to improve the Zeno gate's fidelity via quantum teleportation, establishing bounds for fault-tolerant operation considering mode mismatch and photon transmission ratios.

## Key findings

- Achieves a Zeno CNOT gate with 0.76 success probability at high transmission ratios.
- Demonstrates the potential for fault-tolerant operation with realistic mode-mismatch parameters.
- Provides bounds on mode overlap and transmission ratios necessary for fault tolerance.

## Abstract

In principle the Zeno effect controlled-sign gate of Franson et al's (PRA 70, 062302, 2004) is a deterministic two-qubit optical gate. However, when realistic values of photon loss are considered its fidelity is significantly reduced. Here we consider the use of measurement based quantum processing techniques to enhance the operation of the Zeno gate. With the help of quantum teleportation, we show that it is possible to achieve a Zeno CNOT gate (GC-Zeno gate) that gives (near) unit fidelity and moderate probability of success of 0.76 with a one-photon to two-photon transmission ratio $\kappa=10^4$. We include some mode-mismatch effects and estimate the bounds on the mode overlap and $\kappa$ for which fault tolerant operation would be possible.