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Open AccessArticle

Agents, Subsystems, and the Conservation of Information

by Giulio Chiribella 1,2,3,4
1
Department of Computer Science, University of Oxford, Parks Road, Oxford OX1 3QD, UK
2
Canadian Institute for Advanced Research, CIFAR Program in Quantum Information Science, 661 University Ave, Toronto, ON M5G 1M1, Canada
3
Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China
4
HKU Shenzhen Institute of Research and Innovation, Yuexing 2nd Rd Nanshan, Shenzhen 518057, China
Entropy 2018, 20(5), 358; https://doi.org/10.3390/e20050358
Received: 12 March 2018 / Revised: 26 April 2018 / Accepted: 5 May 2018 / Published: 10 May 2018
(This article belongs to the Special Issue Quantum Information and Foundations)
Dividing the world into subsystems is an important component of the scientific method. The choice of subsystems, however, is not defined a priori. Typically, it is dictated by experimental capabilities, which may be different for different agents. Here, we propose a way to define subsystems in general physical theories, including theories beyond quantum and classical mechanics. Our construction associates every agent A with a subsystem S A , equipped with its set of states and its set of transformations. In quantum theory, this construction accommodates the notion of subsystems as factors of a tensor product, as well as the notion of subsystems associated with a subalgebra of operators. Classical systems can be interpreted as subsystems of quantum systems in different ways, by applying our construction to agents who have access to different sets of operations, including multiphase covariant channels and certain sets of free operations arising in the resource theory of quantum coherence. After illustrating the basic definitions, we restrict our attention to closed systems, that is, systems where all physical transformations act invertibly and where all states can be generated from a fixed initial state. For closed systems, we show that all the states of all subsystems admit a canonical purification. This result extends the purification principle to a broader setting, in which coherent superpositions can be interpreted as purifications of incoherent mixtures. View Full-Text
Keywords: subsystem; agent; conservation of information; purification; group representations; commuting subalgebras subsystem; agent; conservation of information; purification; group representations; commuting subalgebras
MDPI and ACS Style

Chiribella, G. Agents, Subsystems, and the Conservation of Information. Entropy 2018, 20, 358.

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