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From Rényi entropy power to information scan of quantum states

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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 Prokš
In 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

File Version

  • Published version

Journal

Entropy

ISSN

1099-4300

Publisher

MDPI

Issue

3

Volume

23

Page range

1-24

Article number

a334

Department affiliated with

  • Physics and Astronomy Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2021-03-11

First Open Access (FOA) Date

2021-03-23

First Compliant Deposit (FCD) Date

2021-03-11

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