Next Article in Journal
Multiscale Distribution Entropy and t-Distributed Stochastic Neighbor Embedding-Based Fault Diagnosis of Rolling Bearings
Next Article in Special Issue
Solutions of a Two-Particle Interacting Quantum Walk
Previous Article in Journal
Exponential Entropy for Simplified Neutrosophic Sets and Its Application in Decision Making
Previous Article in Special Issue
A No-Go Theorem for Observer-Independent Facts
Article Menu
Issue 5 (May) cover image

Export Article

Open AccessArticle
Entropy 2018, 20(5), 358; https://doi.org/10.3390/e20050358

Agents, Subsystems, and the Conservation of Information

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
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)
  |  
PDF [580 KB, uploaded 17 May 2018]

Abstract

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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top