For a bipartite system governed by a Hamiltonian, one can calculate the evolution of one part. This could be described by a linear non-Hamiltonian process. The general formalism of this is the method of stochastic maps. Sudarshan had formulated this in the early sixties under the title "Stochastic Processes in Quantum Mechanics". A decade later, along with Gorini and Kossakowski he developed the theory of stochastic semigroups.

The generally accepted view was that such maps had to be "completely positive". Such maps can be obtained by the contraction of the unitary evolution of an extended simply separable (i.e., a bipartite unentangled) system; Jordan, Shaji, and Sudarshan showed that this is not valid for entangled bipartite systems by explicit calculations.

The separability of a bipartite system state is of interest in Quantum Computing. For the past decade, Sudarshan has been studying various aspects of this; and his students have studied the detailed evolution of bipartite systems and the methods of controlling decoherence.

With the von Neumann postulates a quantum measurement gives one or other possible values with a probability dictated by the state. The first such model was constructed by Sudarshan in which he coupled a classical system with a quantum system by an explicit Hamiltonian. The basic Stern-Gerlach experiment was studied in detail within this framework.

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