Do we really need to define geometric phase for mixed states? The Quantum jump approach A system interacting with an enviroment the state evolves according d, to the master equation =-H,]+∑2rpr Tp dt By dividing the time into small steps At the evolution can be cast into this form p+△r)=∑WpP(Wy iere “ No-jump” operator W=√△ -th jump operator A C. M. Franca Santos, I. Fuentes-Guiridi V. Vedral. PRL 200318 Do we really need to define geometric phase for mixed states? • A system interacting with an enviroment the state evolves according to the master equation: • By dividing the time into small steps Δt, the evolution can be cast into this form: where = −  +(   −   −  ) + + + i H i i i i i i i dt d      , 2 0 1 i i i W iH t   + = − −         W t i i =   i-th jump operator “No-jump” operator The Quantum jump approach ( )  + +  = i i Wi  t t W (t) A.C., M. Franca Santos, I. Fuentes-Guiridi, V. Vedral, PRL 2003