Nondemolition Continuous Measurement and the Quantum Stochastic Differential Equations

敏彦 有光, 幸夫 遠藤

Ricardo Castro Santis, Alberto Barchielli

Alberto Barchielli, Anna Maria Paganoni

Alberto Barchielli, Anna Maria Paganoni

The theory of measurements continuous in time in quantum mechanics (quantum continual measurements) has been formulated by using the notions of instrument and positive operator valued measure [ 1 , 2 , 3 , 4 , 5 , 6 ], arisen inside the operational approach [ 1 , 7 ] to quantum mechanics, by using functional integrals [ 8 , 9 , 10 ], by using quantum stochastic differential equations [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ] and by using classical stochastic differential equations (SDE’s) [ 12 , 13 , 14 , 15 , 16 , 17 , 18 , 4 , 19 , 20 , 21 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 6 ]. Various types of SDE’s are involved, and precisely linear and non linear equations for vectors in Hilbert spaces and for trace-class operators. All such equations contain either a diffusive part, or a jump one, or both.

Alberto Barchielli

Alberto Barchielli

Continuous (in time) measurements can be introduced in quantum mechanics by using operation-valued measures and quantum stochastic calculus. In this paper quantum stochastic calculus is used for showing the connections between measurement theory and open-system theory. In particular, it is shown how continuous measurements are strictly related to the concept of output channels, introduced in the framework of quantum stochastic differential equations by Gardiner and Collet.