Incompatibility as a Resource for Programmable Quantum Instruments

Journal Article · 06 March 2024 · PRX Quantum

DOI: https://doi.org/10.1103/PRXQuantum.5.010340 · OSTI ID:2320323

Ji, Kaiyuan ; Chitambar, Eric

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. Published by the American Physical Society 2024

• Research Organization: National Quantum Information Science (QIS) Research Centers (United States). Next Generation Quantum Science and Engineering (Q-NEXT)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 2320323
• Journal Information: PRX Quantum, Journal Name: PRX Quantum Journal Issue: 1 Vol. 5; ISSN 2691-3399; ISSN PQRUAG
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English