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

作者：Kang, Yuanbao^*; Wang, Caishi

来源：Physica A: Statistical Mechanics and Its Applications , 2014, 414: 154-162.

DOI：10.1016/j.physa.2014.06.086

• DQRW
• CQRW
• Ito formula
• Tanaka's formula

In the paper, we first extend the discrete time quantum random walk (DQRW) to continuous time quantum random walk (CQRW). Then we establish an Ito formula for the one-dimensional CQRW. As an application, we present Tanaka's formula with the Ito formula and characterize the relation between quantum local time L-t(a) and Dirac delta function delta. Finally, we discuss quantum stochastic calculus for the CQRW.

• 单位
  西北师范大学