Quantum stochastic calculus is a generalization of stochastic calculus to noncommuting variables.[1] The tools provided by quantum stochastic calculus are of great use for modeling the random evolution of systems undergoing measurement, as in quantum trajectories.[2]: 148 Just as the Lindblad master equation provides a quantum generalization to the Fokker–Planck equation, quantum stochastic calculus allows for the derivation of quantum stochastic differential equations (QSDE) that are analogous to classical Langevin equations.
For the remainder of this article stochastic calculus will be referred to as classical stochastic calculus, in order to clearly distinguish it from quantum stochastic calculus.
- ^ Hudson, R. L.; Parthasarathy, K. R. (1984-09-01). "Quantum Ito's Formula and Stochastic Evolutions". Communications in Mathematical Physics. 93 (3): 301–323. Bibcode:1984CMaPh..93..301H. doi:10.1007/BF01258530. S2CID 122848524.
- ^ Wiseman, Howard M.; Milburn, Gerard J. (2010). Quantum Measurement and Control. New York: Cambridge University Press. ISBN 978-0-521-80442-4.