# 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

, Volume 16 (5) – Mar 23, 2017
33 pages

/lp/springer_journal/real-time-simulation-of-h-p-noisy-schr-dinger-equation-and-belavkin-2PIXlqeLJt
Publisher
Springer US
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

## 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
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. ### Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. ### Organize your research It’s easy to organize your research with our built-in tools. ### 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. ### Monthly Plan • Read unlimited articles • Personalized recommendations • No expiration • Print 20 pages per month • 20% off on PDF purchases • Organize your research • Get updates on your journals and topic searches$49/month

14-day Free Trial

Best Deal — 39% off

### Annual Plan

• All the features of the Professional Plan, but for 39% off!
• Billed annually
• No expiration
• For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588$360/year

billed annually

14-day Free Trial