Efficient construction of witnesses of stellar rank of nonclassical states of light

TL;DR

This paper introduces an efficient method to construct witnesses for the stellar rank of nonclassical light states, enabling better characterization of quantum resources with scalable parameter optimization.

Contribution

The authors develop a scalable, parameter-efficient approach for constructing stellar rank witnesses applicable to multi-mode quantum states of light.

Findings

Parameter count for witnesses is independent of stellar rank.

Method scales quadratically with the number of modes.

Constructed witnesses based on Fock state probabilities and coherent state fidelities.

Abstract

The stellar hierarchy of quantum states of light classifies the states according to the Fock-state resources that are required for their generation together with unitary Gaussian operations. States with stellar rank n can be also equivalently referred to as genuinely n-photon quantum non-Gaussian states. Here we present an efficient method for construction of general witnesses of the stellar rank. The number of parameters that need to be optimized in order to determine the witness does not depend on the stellar rank and it scales quadratically with the number of modes. We illustrate the procedure by constructing stellar rank witnesses based on pairs of Fock state probabilities and also based on pairs of fidelities with superpositions of coherent states.