# Entanglement quantification from incomplete measurements: Applications using photon-number-resolving weak homodyne detectors

## TL;DR

This paper demonstrates that photon-number-resolving weak homodyne detectors can efficiently estimate entanglement bounds in two-mode states, reducing resource needs compared to full state tomography.

## Contribution

It introduces a novel measurement approach combining phase sensitivity and photon-number resolution to bound entanglement without full state reconstruction.

## Key findings

- Tight lower bounds on entanglement can be achieved with few measurements.
- The method outperforms traditional tomography in resource efficiency.
- Applicable to continuous-variable entanglement distillation protocols.

## Abstract

The certificate of success for a number of important quantum information processing protocols, such as entanglement distillation, is based on the difference in the entanglement content of the quantum states before and after the protocol. In such cases, effective bounds need to be placed on the entanglement of non-local states consistent with statistics obtained from local measurements. In this work, we study numerically the ability of a novel type of homodyne detector which combines phase sensitivity and photon-number resolution to set accurate bounds on the entanglement content of two-mode quadrature squeezed states without the need for full state tomography. We show that it is possible to set tight lower bounds on the entanglement of a family of two-mode degaussified states using only a few measurements. This presents a significant improvement over the resource requirements for the experimental demonstration of continuous-variable entanglement distillation, which traditionally relies on full quantum state tomography.