A general theory of comparison of quantum channels (and beyond)
Anna Jenčová
备注：
32 pages, comments welcome. A part of the paper was presented at the Algebraic and Statistical ways into Quantum Resource Theories workshop at BIRS in July 2019. Extended and revised, the case of LOCC superchannels added
发表信息：
IEEE Transactions on Information Theory, vol. 67, no. 6, pp. 3945-3964, 2021
We present a general theory of comparison of quantum channels, concerning with the question of simulability or approximate simulability of a given quantum channel by allowed transformations of another given channel. We introduce a modification of conditional min-entropies, with respect to the set F of allowed transformations, and show that under some conditions on F, these quantities characterize approximate simulability. If F is the set of free superchannels in a quantum resource theory of processes, the modified conditional min-entropies form a complete set of resource monotones. If the transformations in F consist of a preprocessing and a postprocessing of specified forms, approximate simulability is also characterized in terms of success probabilities in certain guessing games, where a preprocessing of a given form can be chosen and the measurements are restricted. These results are applied to several specific cases of simulability of quantum channels, including postprocessings, preprocessings and processing of bipartite channels by LOCC superchannels and by partial superchannels, as well as simulability of sets of quantum measurements.
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QudeLeap Research, Shanghai 200030, China（科跃研究）；Thrust of Artificial Intelligence, Information Hub,The Hong Kong University of Science and Technology (Guangzhou), Guangzhou 511453, China（香港科技大学（广州）人工智能 thrust 信息枢纽）
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Institute for Quantum Inspired and Quantum Optimization, Hamburg University of Technology（汉堡工业大学量子启发与量子优化研究所）；University of Tsukuba（筑波大学）；Center for Artificial Intelligence Research (C-AIR), University of Tsukuba（筑波大学人工智能研究中心）
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