# Entanglement verification of noisy N00N states

## TL;DR

This paper investigates the entanglement properties of noisy N00N states, using novel detection methods to determine when their quantum features can be reliably utilized despite imperfections and environmental effects.

## Contribution

It introduces a comprehensive approach for verifying entanglement in noisy N00N states, including the use of entanglement quasiprobabilities for full characterization.

## Key findings

- Entanglement persists under certain fluctuating loss conditions.
- Gaussian dephasing affects entanglement detection.
- Methods enable entanglement verification in realistic noisy scenarios.

## Abstract

Entangled quantum states, such as N00N states, are of major importance for quantum technologies due to their quantum-enhanced performance. At the same time, their quantum correlations are relatively vulnerable when they are subjected to imperfections. Therefore, it is crucial to determine under which circumstances their distinct quantum features can be exploited. In this paper, we study the entanglement property of noisy N00N states. This class of states is a generalization of N00N states including various attenuation effects, such as mixing, constant or fluctuating losses, and dephasing. To verify their entanglement, we pursue two strategies: detection-based entanglement witnesses and entanglement quasiprobabilities. Both methods result from our solution of so-called separability eigenvalue equations. In particular, the entanglement quasiprobabilities allow for a full entanglement characterization. As examples of our general treatment, the cases of N00N states subjected to Gaussian dephasing and fluctuating atmospheric losses are explicitly studied. In any correlated fluctuating loss channel, entanglement is found to survive for non-zero transmissivity. In addition, an extension of our approach to multipartite systems is given, and the relation to the quantum-optical nonclassicality in phase-space is discussed.