Fidelity-disturbance-entropy tradeoff in quantum channels

Yuan Sun, Nan Li, and Shunlong Luo
Phys. Rev. A 105, 062458 – Published 29 June 2022

Abstract

Quantum channels are indispensable instruments for transmitting, extracting, and processing information. According to the spirit of the Bohr complementarity principle and the Heisenberg uncertainty principle, one expects that there are intrinsic tradeoff relations between state disturbance and information gain for any channel, which indeed have been widely studied and characterized from various angles. In this work, we investigate this issue from the perspective of information conservation. More specifically, we divide the information associated with a channel into three categories: transmitted information (quantified by operation fidelity), disturbance (quantified by the Hilbert-Schmidt norm), and extracted information (quantified by the increase of Tsallis-2 entropy), which are all derived naturally from a channel with direct physical motivations. We reveal basic properties of these three information-theoretic quantities and establish a triality relation between them. As applications, we apply these quantities to shed insights into the Mach-Zehnder interferometry and several prototypical channels.

  • Figure
  • Figure
  • Received 27 March 2022
  • Accepted 17 June 2022

DOI:https://doi.org/10.1103/PhysRevA.105.062458

©2022 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Yuan Sun*

  • School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China

Nan Li and Shunlong Luo

  • Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

  • *sunyuan@njnu.edu.cn
  • linan@amss.ac.cn
  • luosl@amt.ac.cn

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Issue

Vol. 105, Iss. 6 — June 2022

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