# Benchmarking maximum-likelihood state estimation with an entangled two-cavity state

## TL;DR

This paper experimentally benchmarks a maximum-likelihood quantum state estimation method on an entangled two-cavity system, demonstrating high accuracy and robustness in reconstructing complex quantum states with realistic error analysis.

## Contribution

It implements and validates an efficient quantum state reconstruction algorithm on a non-local entangled cavity system, combining multiple measurement protocols for improved accuracy.

## Key findings

- Successful reconstruction of entangled cavity states
- Realistic error bars for density matrix elements
- Demonstration of method's applicability to complex quantum systems

## Abstract

The efficient quantum state reconstruction algorithm described in [P. Six et al., Phys. Rev. A 93, 012109 (2016)] is experimentally implemented on the non-local state of two microwave cavities entangled by a circular Rydberg atom. We use information provided by long sequences of measurements performed by resonant and dispersive probe atoms over time scales involving the system decoherence. Moreover, we benefit from the consolidation, in the same reconstruction, of different measurement protocols providing complementary information. Finally, we obtain realistic error bars for the matrix elements of the reconstructed density operator. These results demonstrate the pertinence and precision of the method, directly applicable to any complex quantum system.