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.
Highlights
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
Beyond the problem of characterizing resourceful states mathematically, the experimental detection and quantification of resource states is further complicated by the lack of a general theory to devise efficient measurement protocols. Such protocols would allow one to decide, at minimum experimental cost, whether a source is capable of producing resourceful states. Developing such methods is important for high dimensional systems where full tomography is infeasible or in cases where the resource states to be detected are restricted to a small subset of the state space, which renders tomography excessive
We propose the framework of quantum preparation games to reason about the detection and quantification of resource states in this adaptive setting
Summary
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. General results on the optimal discrimination between different sets of states in the asymptotic regime[6] suggest that the optimal measurement protocol usually involves collective measurements over many copies of the states of interest, and would require a quantum memory for its implementation This contrasts with the measurement scenario encountered in many experimental setups: the lack of a quantum memory often forces an experimentalist to measure each of the prepared states as soon as they arrive at the lab. We illustrate all our techniques with examples from entanglement certification and quantification and highlight the benefit of adaptive measurement strategies in various ways In this regard, in contradiction to standard practice in entanglement detection, we find that the optimal n-round measurement protocol to detect the entanglement of a single, known quantum state does not consist in estimating n times the value of a given (optimised) entanglement witness. There exist adaptive measurement schemes that supersede any non-adaptive protocol for this task
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