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Title: The uncertainty principle of quantum processes
Authors: Xiao, Yunlong
Sengupta, Kuntal
Yang, Siren
Gour, Gilad
Keywords: Science::Physics
Issue Date: 2021
Source: Xiao, Y., Sengupta, K., Yang, S. & Gour, G. (2021). The uncertainty principle of quantum processes. Physical Review Research, 3(2), 023077-1-023077-11.
Project: NRF-NRFF2016-02 
Journal: Physical Review Research
Abstract: Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and quantum mechanics. The physical systems considered in the uncertainty principle are static in nature and described mathematically with a quantum state in a Hilbert space. However, many physical systems are dynamic in nature and described with the formalism of a quantum channel. In this paper, we show that the uncertainty principle can be reformulated to include process-measurements that are performed on quantum channels. Since both quantum states and quantum measurements are themselves special cases of quantum channels, our formalism encapsulates the uncertainty principle in its utmost generality. More specifically, we obtain expressions that generalize the Maassen-Uffink uncertainty relation and the universal uncertainty relations from quantum states to quantum channels.
ISSN: 2643-1564
DOI: 10.1103/PhysRevResearch.3.023077
Schools: School of Physical and Mathematical Sciences 
Research Centres: Complexity Institute 
Rights: © 2021 The Authors. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the authors and the published article’s title, journal citation, and DOI.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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