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Open Quantum Systems Decoherence Quantum Simulation Quantum State Preparation Representation Entanglement Theory Quantum Correlations

Multiple Q-Adapted Integrals and Ito Formula of Noncommutative Stochastic Calculus in Fock Space

arXiv
Authors: Viacheslav P. Belavkin, Matthew F. Brown

Year

2011

Paper ID

29452

Status

Preprint

Abstract Read

~2 min

Abstract Words

78

Citations

N/A

Abstract

We study the continuity property of multiple Q-adapted quantum stochastic integrals with respect to noncommuting integrands given by the non-adapted multiple integral kernels in Fock scale. The noncommutative algebra of relatively (exponentially) bounded nonadapted quantum stochastic processes is studied in the kernel form as introduced by Belavkin in 1991. The differential Q-adapted formula generalizing Ito product formula for adapted integrals is presented in both strong and weak sense as a particular case of the quantum stochastic nonadapted Ito formula.

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  • We study the continuity property of multiple Q-adapted quantum stochastic integrals with respect to noncommuting integrands given by the non-adapted multiple integral kernels...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1112.0159 [2] arXiv https://arxiv.org/abs/1112.0159 [3] Publisher https://arxiv.org/abs/1112.0159

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