# Heralded orthogonalisation of coherent states and their conversion to discrete-variable superpositions

## TL;DR

This paper introduces a feasible probabilistic protocol for orthogonalising coherent states without destroying them, enabling their use in hybrid quantum information processing and approximating discrete-variable superpositions.

## Contribution

The authors present a novel, experimentally feasible method for heralded orthogonalisation of coherent states, independent of amplitude and phase, useful for quantum information protocols.

## Key findings

- Protocol successfully orthogonalises coherent states probabilistically
- Orthogonalised states approximate discrete-variable superpositions
- Operation is heralded and non-destructive, suitable for further processing

## Abstract

The nonorthogonality of coherent states is a fundamental property which prevents them from being perfectly and deterministically discriminated. To circumvent this problem, we present an experimentally feasible protocol for the probabilistic orthogonalisation of a pair of coherent states, independent of their amplitude and phase. In contrast to unambiguous state discrimination, successful operation of our protocol is heralded without measuring the states, such that they remain suitable for further manipulation. As such, the resulting orthogonalised state may be used for further processing. Indeed, these states are close approximations of the discrete-variable superposition state $\frac{1}{\sqrt{2}}\left(|0\rangle \pm |1\rangle\right)$. This feature, coupled with the non-destructive nature of the operation, is especially useful when considering superpositions of coherent states: such states are mapped to the (weakly squeezed) vacuum or single photon Fock state, depending on the phase of the superposition. Thus this operation may find utility in hybrid continuous-discrete quantum information processing protocols.