How to improve the discrimination power of classically simulable measurements?

In quantum information theory, Classically Simulable Measurements (CSMs)—defined as measurements with positive discrete Wigner functions—are restricted compared to global measurements. This paper investigates how to bridge the gap in discrimination power between CSMs and global measurements. Specifically, the authors explore whether adding magic resources, quantum catalysts, or quantum memories can enhance the success probability of discriminating quantum states using CSMs.

The authors establish a formal equivalence between CSMs and completely positive Wigner-preserving (CPWP) measurement channels. By mapping the problem of measurement discrimination to a channel simulation task, they derive lower and upper bounds on the "magic cost" required to simulate measurements beyond the CSM limit. They also formulate the magic-assisted discrimination problem as a semidefinite program (SDP) to compute optimal success probabilities. Finally, they analyze the utility of reusable resources (catalysts and memories) in this context.

The study provides a concrete example using the qutrit Strange state to demonstrate that consumable magic resources can strictly improve the discrimination power of CSMs. However, the authors establish a no-go theorem proving that for a pair of states with positive Wigner functions, neither finite-dimensional quantum catalysts nor finite-dimensional quantum memories can improve the optimal success probability of discrimination. This suggests that while "spending" magic resources is effective, simply recycling auxiliary systems through catalysis or memory does not overcome the fundamental limitations of CSMs in this specific resource theory.