Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes

Physical Review. E
Carlo Cafaro, Paul M Alsing

Abstract

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geo...Continue Reading

References

Apr 1, 1989·Physical Review A: General Physics·K H HoffmannP Salamon
Apr 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·B R Frieden, R J Hughes
Dec 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·B Andresen, J M Gordon
Feb 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·D Brody, N Rivier
Sep 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·B R Frieden, B H Soffer
Oct 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·W Spirkl, H Ries
Jul 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·B R Frieden, W J Cocke
May 30, 1994·Physical Review Letters·S L Braunstein, C M Caves
Nov 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B R FriedenB H Soffer
Aug 26, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S P FlegoB H Soffer
Nov 13, 2003·Physical Review Letters·Shunlong Luo
Jul 13, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F Pennini, A Plastino
Oct 26, 2005·Physical Review Letters·Lov K Grover
Feb 21, 2006·Physical Review Letters·Vittorio GiovannettiLorenzo Maccone
Apr 12, 2006·Physical Review Letters·Alberto CarliniYosuke Okudaira
Mar 16, 2007·Physical Review Letters·Sergio BoixoJ M Geremia
Oct 13, 2007·Physical Review Letters·Gavin E Crooks
Oct 13, 2007·Physical Review Letters·Gabriel A Durkin, Jonathan P Dowling
Mar 21, 2008·Physical Review Letters·S Boixo, A Monras
Mar 21, 2008·Physical Review Letters·M H S AminC J S Truncik
Apr 28, 2009·Physical Review Letters·Luca Pezzé, Augusto Smerzi
Jun 13, 2009·Physical Review Letters·Ari Mizel
Oct 2, 2009·Physical Review Letters·A T RezakhaniP Zanardi
Sep 26, 2012·Physical Review Letters·David A Sivak, Gavin E Crooks
Feb 19, 2013·Physical Review Letters·M M TaddeiR L de Matos Filho
Feb 19, 2013·Physical Review Letters·A del CampoS F Huelga
Jul 19, 2013·Physical Review Letters·Sebastian Deffner, Eric Lutz
Mar 18, 2016·Physical Review. E·Carlo CafaroAdom Giffin
Dec 15, 2016·Physical Review. E·Carlo Cafaro, Sean Alan Ali
Mar 25, 2017·Physical Review Letters·Steve Campbell, Sebastian Deffner
Mar 31, 2017·Nature·Davide Castelvecchi
Feb 27, 2018·Physical Review Letters·Tim ByrnesLouis Tessler
Apr 2, 2018·Chaos·Domenico FeliceStefano Mancini

❮ Previous
Next ❯

Citations


❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Medical Image Computing and Computer-assisted Intervention : MICCAI
Jian ChengRachid Deriche
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Prashant KumarTapobrata Sarkar
Physical Review Letters
A T RezakhaniPaolo Zanardi
© 2022 Meta ULC. All rights reserved