Optimal state estimaion in Arthurs-Kelly scheme with modified Hamiltonian

Arthurs and Kelly considered the joint measurement of conjugate observables, which eventually resolved the dilemma surrounding various uncertainty principles. They extended the von Neumann model, where the system was coupled with two detectors using an interaction Hamiltonian. In this work, we further advance the research by modifying the interaction Hamiltonian, leading to correlated detectors [1]. Our analysis shows that the optimal state estimation corresponds to uncorrelated detectors. These results enhance our understanding of the uncertainties associated with joint measurements of conjugate observables in a general situation and will be of direct relevance in various quantum protocols in the area of continuous-variable quantum information processing. Phase space techniques and the application of the real symplectic group Sp(6, R) significantly simplify the analysis [2].

Ref:
[1] P. Busch, "Indeterminacy relations and simultaneous measurements in quantum theory", IJTP, 24(1), (Jan 1985).
[2] Arvind, S. Chaturvedi, and N. Mukunda, "Symplectic group methods and the Arthurs Kelly model of measurement in quantum mechanics", Physics Letters A, 384(23), (2020).