The uncertainty principle of quantum processes
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...
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sg-ntu-dr.10356-1607012023-02-28T20:07:20Z The uncertainty principle of quantum processes Xiao, Yunlong Sengupta, Kuntal Yang, Siren Gour, Gilad School of Physical and Mathematical Sciences Complexity Institute Science::Physics Arbitrary Precision Heisenberg's Uncertainty Principle 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. Ministry of Education (MOE) National Research Foundation (NRF) Published version Y.X. and G.G. acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC). Y.X. is supported by the National Research Foundation (NRF) Singapore, under its NRFF Fellow programme (Grant No. NRF-NRFF2016-02), Singapore Ministry of Education Tier 1 Grant No. MOE2017-T1-002-043 from the Foundational Questions Institute and Fetzer Franklin Fund Grant No. FQXi-RFP-1809 (a donor-advised fund of Silicon Valley Community Foundation). 2022-08-01T05:02:25Z 2022-08-01T05:02:25Z 2021 Journal Article Xiao, Y., Sengupta, K., Yang, S. & Gour, G. (2021). The uncertainty principle of quantum processes. Physical Review Research, 3(2), 023077-1-023077-11. https://dx.doi.org/10.1103/PhysRevResearch.3.023077 2643-1564 https://hdl.handle.net/10356/160701 10.1103/PhysRevResearch.3.023077 2-s2.0-85115897549 2 3 023077-1 023077-11 en NRF-NRFF2016-02 MOE2017-T1-002-043 Physical Review Research © 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. application/pdf |
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Science::Physics Arbitrary Precision Heisenberg's Uncertainty Principle Xiao, Yunlong Sengupta, Kuntal Yang, Siren Gour, Gilad The uncertainty principle of quantum processes |
description |
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. |
author2 |
School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Xiao, Yunlong Sengupta, Kuntal Yang, Siren Gour, Gilad |
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Article |
author |
Xiao, Yunlong Sengupta, Kuntal Yang, Siren Gour, Gilad |
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Xiao, Yunlong |
title |
The uncertainty principle of quantum processes |
title_short |
The uncertainty principle of quantum processes |
title_full |
The uncertainty principle of quantum processes |
title_fullStr |
The uncertainty principle of quantum processes |
title_full_unstemmed |
The uncertainty principle of quantum processes |
title_sort |
uncertainty principle of quantum processes |
publishDate |
2022 |
url |
https://hdl.handle.net/10356/160701 |
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1759855340928630784 |