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Itô formula for one-dimensional continuous-time quantum random walk

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  • Kang, Yuanbao
  • Wang, Caishi

Abstract

In the paper, we first extend the discrete time quantum random walk (DQRW) to continuous time quantum random walk (CQRW). Then we establish an Itô formula for the one-dimensional CQRW. As an application, we present Tanaka’s formula with the Itô formula and characterize the relation between quantum local time Lta and Dirac delta function δ. Finally, we discuss quantum stochastic calculus for the CQRW.

Suggested Citation

  • Kang, Yuanbao & Wang, Caishi, 2014. "Itô formula for one-dimensional continuous-time quantum random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 154-162.
    • Handle: RePEc:eee:phsmap:v:414:y:2014:i:c:p:154-162
    DOI: 10.1016/j.physa.2014.06.086
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    References listed on IDEAS

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    1. Da Pelo, Paolo & Lanconelli, Alberto & Stan, Aurel I., 2013. "An Itô formula for a family of stochastic integrals and related Wong–Zakai theorems," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3183-3200.
    2. Biane, Philippe, 2010. "Itô's stochastic calculus and Heisenberg commutation relations," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 698-720, May.
    3. Kunita, Hiroshi, 2010. "Itô's stochastic calculus: Its surprising power for applications," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 622-652, May.
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    Cited by:

    1. Kang, Yuanbao, 2016. "Quantum decomposition of random walk on Cayley graph of finite group," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 146-156.

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