Construction of efficient Schmidt number witnesses for high-dimensional quantum states

TL;DR

This paper introduces an iterative algorithm to construct efficient Schmidt number witnesses tailored for high-dimensional quantum states, enabling better benchmarking of entanglement in quantum optics experiments.

Contribution

It develops a novel iterative method for designing Schmidt number witnesses that are optimized for specific measurement setups in high-dimensional quantum systems.

Findings

The algorithm finds witnesses requiring linearly scaling measurements with system dimension.

Applied to photonic temporal modes, demonstrating practical implementation.

Enhances the ability to benchmark entanglement in high-dimensional quantum states.

Abstract

Recent progress in quantum optics has led to setups that are able to prepare high-dimensional quantum states for quantum information processing tasks. As such, it is of importance to benchmark the states generated by these setups in terms of their quantum mechanical properties, such as their Schmidt numbers, i.e., the number of entangled degrees of freedom. In this paper, we develop an iterative algorithm that finds Schmidt number witnesses tailored to the measurements available in specific experimental setups. We then apply the algorithm to find a witness that requires the measurement of a number of density matrix elements that scales linearly with the local dimension of the system. As a concrete example, we apply our construction method to an implementation with photonic temporal modes.