Incompatibility as a resource for programmable quantum instruments

Abstract

Quantum instruments represent the most general type of quantum measurement, as they incorporate processes with both classical and quantum outputs. In many scenarios, it may be desirable to have some "on-demand" device that is capable of implementing one of many possible instruments whenever the experimenter desires. We refer to such objects as programmable instrument devices (PIDs), and this paper studies PIDs from a resource-theoretic perspective. A physically important class of PIDs are those that do not require quantum memories to implement, and these are naturally "free" in this resource theory. Additionally, these free objects correspond precisely to the class of unsteerable channel assemblages in the study of channel steering. The traditional notion of measurement incompatibility emerges as a resource in this theory since any PID controlling an incompatible family of instruments requires a quantum memory to build. We identify an incompatibility preorder between PIDs based on whether one can be transformed into another using processes that do not require additional quantum memories. Necessary and sufficient conditions are derived for when such transformations are possible based on how well certain guessing games can be played using a given PID. Ultimately our results provide an operational characterization of incompatibility, and they offer semi-device-independent tests for incompatibility in the most general types of quantum instruments.

28 pages, 15 figures, published version

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Cited by in corpus (8)

• Thermodynamic Approach to Quantifying Incompatible Instruments
• Dynamical Landauer principle: Thermodynamic criteria of transmitting classical information
• One-shot manipulation of coherence in dynamic quantum resource theory
• Multi-object operational tasks for measurement incompatibility
• Resource theory of interactive quantum instruments
• Weight-based measure of quantum memory as a universal and operational benchmark
• Entropic and operational characterizations of dynamic quantum resources
• A resource theory of asynchronous quantum information processing