Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1011.4637

A quantum stochastic Lie-Trotter product formula

J. Martin Lindsay, Kalyan B. Sinha

Published Nov 21, 2010• 0 citations
arXivHTMLPDF

Abstract

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.
DOI
10.48550/arxiv.1011.4637

Related papers

A Trotter Product Formula for quantum stochastic flows

B. Krishna Das, Debashish Goswami, Kalyan B. Sinha

We give a new method for proving the homomorphic property of a quantum stochastic ow satisfying a quantum stochastic differential equation with unbounded coefficients, under some further hypotheses. As an application, we prove a Trotter product formula for quantum stochastic ows and obtain quantum stochastic dilations of a class of quantum dynamical semigroups generalizing results of [5]

•Jan 1, 2010•2 citations

A quantum stochastic Lie-Trotter product formula

J. Martin Lindsay, Kalyan B. Sinha

Indian Journal of Pure and Applied Mathematics•Feb 1, 2010•10 citations

A Homomorphism Theorem and a Trotter Product Formula for Quantum Stochastic Flows with Unbounded Coefficients

Biswarup Das, Debashish Goswami, Kalyan B. Sinha

arXiv:1001.0233•Communications in Mathematical Physics•Mar 18, 2014•5 citations

AN ANALYTIC DOUBLE PRODUCT INTEGRAL

R. L. Hudson

Abstract. The double product integral → ← ∏ (1+λ(dA † ⊗dA−dA⊗dA †)) is constructed as a family of unitary operators in double Fock space satisfying quantum stochastic differential equations with unbounded operator coefficients. 1. Introduction. A purely algebraic theory of double product integrals such as → ← ∏ (1 + λ(dA ⊗ dA − dA ⊗ dA †)) [4][9] has been developed based on formal power series in the formal

Quantum Probability and Infinite Dimensional Analysis•Jul 1, 2007•4 citations

Quantum Stochastic Lie–Trotter Product Formula II

J. Martin Lindsay

A natural counterpart to the Lie–Trotter product formula for norm-continuous, one-parameter semigroups is proved, for the class of quasicontractive quantum stochastic (QS) operator cocycles whose expectation semigroup is norm continuous. Compared to previous such results, the assumption of a strong form of independence of the constituent cocycles is overcome. The analysis is facilitated by the development of some quantum Itô algebra. It is also shown how the maximal Gaussian component of a QS generator may be extracted—leading to a canonical decomposition of such generators, and the connection to perturbation theory is described. Finally, the quantum Itô algebra is extended to quadratic form generators, and a conjecture is formulated for the extension of the product formula to holomorphic QS cocycles.

arXiv:1707.05669•International Mathematics Research Notices•Jan 16, 2018•2 citations

Quantum Stochastic Processes

Joseph Spring, Alexander I. Lvovsky

We consider quantum analogues of n‐parameter stochastic processes, associated integrals and martingale properties extending classical results obtained in [1, 2, 3], and quantum results in [4, 5, 6, 7, 8, 9, 10].

AIP conference proceedings•Jan 1, 2009•2 citations
A natural counterpart to the Lie–Trotter product formula for norm-continuous, one-parameter semigroups is proved, for the class of quasicontractive quantum stochastic (QS) operator cocycles whose expectation semigroup is norm continuous. Compared to previous such results, the assumption of a strong form of independence of the constituent cocycles is overcome. The analysis is facilitated by the development of some quantum Itô algebra. It is also shown how the maximal Gaussian component of a QS generator may be extracted—leading to a canonical decomposition of such generators, and the connection to perturbation theory is described. Finally, the quantum Itô algebra is extended to quadratic form generators, and a conjecture is formulated for the extension of the product formula to holomorphic QS cocycles.