Towards optimal experimental tests on the reality of the quantum state

TL;DR

This paper introduces a convex optimisation-based method to design optimal experimental tests for the reality of the quantum state, improving robustness and efficiency in demonstrating the wavefunction's ontological status.

Contribution

It develops a versatile numerical approach to identify optimal state and measurement sets for BCLM tests, accounting for experimental errors and showing mixed states can be more effective.

Findings

Identified improved low-cardinality sets for BCLM tests in low-dimensional systems

Demonstrated mixed states can outperform pure states in these tests

Provided a robust, efficient optimisation framework for experimental design

Abstract

The Barrett-Cavalcanti-Lal-Maroney (BCLM) argument stands as the most effective means of demonstrating the reality of the quantum state. Its advantages include being derived from very few assumptions, and a robustness to experimental error. Finding the best way to implement the argument experimentally is an open problem, however, and involves cleverly choosing sets of states and measurements. I show that techniques from convex optimisation theory can be leveraged to numerically search for these sets, which then form a recipe for experiments that allow for the strongest statements about the ontology of the wavefunction to be made. The optimisation approach presented is versatile, efficient and can take account of the finite errors present in any real experiment. I find significantly improved low-cardinality sets which are guaranteed partially optimal for a BCLM test in low Hilbert space dimension. I further show that mixed states can be more optimal than pure states.