Real-time simulation of H–P noisy Schrödinger equation and Belavkin filter

Real-time simulation of H–P noisy Schrödinger equation and Belavkin filter The Hudson–Parthasarathy noisy Schrödinger equation is an infinite-dimensional differential equation where the noise operators—Creation, Annihilation and Conservation processes—take values in Boson Fock space. We choose a finite truncated basis of exponential vectors for the Boson Fock space and obtained the unitary evolution in a truncated orthonormal basis using the Gram–Schmidt orthonormalization process to the exponential vectors. Then, this unitary evolution is used to obtained the approximate evolution of the system state by tracing out over the bath space. This approximate evolution is compared to the exact Gorini–Kossakowski–Sudarshan–Lindblad equation for the system state. We also perform a computation of the rate of change of the Von Neumann entropy for the system assuming vacuum noise state and derive condition for entropy increase. Finally, by taking non-demolition measurement in the sense of Belavkin, we simulate the Belavkin quantum filter and show that the Frobenius norm of the error observables $$j_t(X)-\pi _t(X)$$ j t ( X ) - π t ( X ) becomes smaller with time for a class of observable X. Here $$j_t(X)$$ j t ( X ) is the H–P equation observable and $$\pi _t(X)$$ π t ( X ) is the Belavkin filter output observable. In last, we have derived an approximate expression for the filtered density and entropy of the system after filtering. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Real-time simulation of H–P noisy Schrödinger equation and Belavkin filter

Loading next page...
 
/lp/springer_journal/real-time-simulation-of-h-p-noisy-schr-dinger-equation-and-belavkin-2PIXlqeLJt
Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-017-1572-4
Publisher site
See Article on Publisher Site

Abstract

The Hudson–Parthasarathy noisy Schrödinger equation is an infinite-dimensional differential equation where the noise operators—Creation, Annihilation and Conservation processes—take values in Boson Fock space. We choose a finite truncated basis of exponential vectors for the Boson Fock space and obtained the unitary evolution in a truncated orthonormal basis using the Gram–Schmidt orthonormalization process to the exponential vectors. Then, this unitary evolution is used to obtained the approximate evolution of the system state by tracing out over the bath space. This approximate evolution is compared to the exact Gorini–Kossakowski–Sudarshan–Lindblad equation for the system state. We also perform a computation of the rate of change of the Von Neumann entropy for the system assuming vacuum noise state and derive condition for entropy increase. Finally, by taking non-demolition measurement in the sense of Belavkin, we simulate the Belavkin quantum filter and show that the Frobenius norm of the error observables $$j_t(X)-\pi _t(X)$$ j t ( X ) - π t ( X ) becomes smaller with time for a class of observable X. Here $$j_t(X)$$ j t ( X ) is the H–P equation observable and $$\pi _t(X)$$ π t ( X ) is the Belavkin filter output observable. In last, we have derived an approximate expression for the filtered density and entropy of the system after filtering.

Journal

Quantum Information ProcessingSpringer Journals

Published: Mar 23, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off