Analysis and optimization of quantum adaptive measurement protocols with the framework of preparation games

Abstract

A preparation game is a task whereby a player sequentially sends a number of quantum states to a referee, who probes each of them and announces the measurement result. Many experimental tasks in quantum information, such as entanglement quantification or magic state detection, can be cast as preparation games. In this paper, we introduce general methods to design n-round preparation games, with tight bounds on the performance achievable by players with arbitrarily constrained preparation devices. We illustrate our results by devising new adaptive measurement protocols for entanglement detection and quantification. Surprisingly, we find that the standard procedure in entanglement detection, namely, estimating n times the average value of a given entanglement witness, is in general suboptimal for detecting the entanglement of a specific quantum state. On the contrary, there exist n-round experimental scenarios where detecting the entanglement of a known state optimally requires adaptive measurement schemes.

Quantum Verification and Estimation with Few Copies

“…In the context of Bell's inequalities, similar kinds of probabilistic protocols are constructed for the single‐shot non‐locality detection [ 70 ] and entanglement detection via preparation games. [ 71 ] In the context of quantum state verification, [ 18,72–74 ] a single‐shot entanglement verification naturally arises in bipartite states as long as the dimension of marginal systems becomes sufficiently large. [ 75,76 ] The generalization to the GHZ states can be found in ref.…”