# Projective measurement onto arbitrary superposition of coherent state bases

## TL;DR

This paper proposes and experimentally implements a method for projecting onto arbitrary superpositions of coherent state bases in optical systems, advancing quantum measurement techniques with potential applications in quantum information processing.

## Contribution

It introduces a novel quantum detector tomography protocol and a practical device for superposition measurements of coherent states in optics.

## Key findings

- Successfully reconstructed measurement operators experimentally.
- Demonstrated projection onto arbitrary superpositions of coherent states.
- Utilized established displacement and photon counting technologies.

## Abstract

One of the peculiar features in quantum mechanics is that a superposition of macroscopically distinct states can exits. In optical system, this is highlighted by a superposition of coherent states (SCS), i.e. a superposition of classical states. Recently this highly nontrivial quantum state and its variant have been demonstrated experimentally. Here we demonstrate the superposition of coherent states in quantum measurement which is also a key concept in quantum mechanics. More precisely, we propose and implement a projection measurement onto the arbitrary superposition of the SCS bases in optical system. The measurement operators are reconstructed experimentally by a novel quantum detector tomography protocol. Our device is realized by combining the displacement operation and photon counting, well established technologies, and thus has implications in various optical quantum information processing applications.