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From Rényi entropy power to information scan of quantum states
Version 2 2023-06-12, 09:45
Version 1 2023-06-09, 23:17
journal contribution
posted on 2023-06-12, 09:45 authored by Petr Jizba, Jacob DunninghamJacob Dunningham, Martin ProkšIn this paper, we generalize the notion of Shannon’s entropy power to the Rényi-entropy setting. With this, we propose generalizations of the de Bruijn identity, isoperimetric inequality, or Stam inequality. This framework not only allows for finding new estimation inequalities, but it also provides a convenient technical framework for the derivation of a one-parameter family of Rényi-entropy-power-based quantum-mechanical uncertainty relations. To illustrate the usefulness of the Rényi entropy power obtained, we show how the information probability distribution associated with a quantum state can be reconstructed in a process that is akin to quantum-state tomography. We illustrate the inner workings of this with the so-called “cat states”, which are of fundamental interest and practical use in schemes such as quantum metrology. Salient issues, including the extension of the notion of entropy power to Tsallis entropy and ensuing implications in estimation theory, are also briefly discussed.
Funding
UK Quantum Technology Hub: NQIT-Networked Quantum Information Technologies; G1503; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/M013243/1
History
Publication status
- Published
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- Published version
Journal
EntropyISSN
1099-4300Publisher
MDPIExternal DOI
Issue
3Volume
23Page range
1-24Article number
a334Department affiliated with
- Physics and Astronomy Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2021-03-11First Open Access (FOA) Date
2021-03-23First Compliant Deposit (FCD) Date
2021-03-11Usage metrics
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