Input-Output Equivalence of Spin Networks under Multiple Measurements

Two quantum control systems that are driven by an external field are said to be input - output equivalent if, for any control field, the measured value of a given observable is the same. Equivalent models cannot be distinguished by experiments involving state evolutions and measurements. In this paper, we characterize the equivalent models of networks of spin 1/2's driven by electro-magnetic fields for which the expectation value of the total magnetization is measured. Extending previous results and definitions that only dealt with the case of a single measurement, we describe the class of equivalent models under a sequence of Von Neumann measurements. The results are motivated by the problem of parameter identification for Heisenberg spin systems modeling molecular magnets.