# Building trust for continuous variable quantum states

## TL;DR

This paper introduces new methods for certifying and verifying continuous variable quantum states using heterodyne measurements, providing reliable, assumption-free protocols with analytical confidence intervals and without data reconstruction.

## Contribution

It presents a novel certification method for continuous variable quantum states and an efficient verification protocol that does not assume identical copies or trust in the state source.

## Key findings

- Reliable certification yields density matrix elements with confidence intervals
- Verification protocol works against fully malicious adversaries
- Method avoids data reconstruction and discrete binning

## Abstract

In this work we develop new methods for the characterisation of continuous variable quantum states using heterodyne measurement in both the trusted and untrusted settings. First, building on quantum state tomography with heterodyne detection, we introduce a reliable method for continuous variable quantum state certification, which directly yields the elements of the density matrix of the state considered with analytical confidence intervals. This method neither needs mathematical reconstruction of the data nor discrete binning of the sample space, and uses a single Gaussian measurement setting. Second, beyond quantum state tomography and without its identical copies assumption, we promote our reliable tomography method to a general efficient protocol for verifying continuous variable pure quantum states with Gaussian measurements against fully malicious adversaries, i.e., making no assumptions whatsoever on the state generated by the adversary. These results are obtained using a new analytical estimator for the expected value of any operator acting on a continuous variable quantum state with bounded support over the Fock basis, computed with samples from heterodyne detection of the state.