Generalized measurement of the non-normal two-boson operator
Matteo G. A. Paris, Giulio Landolfi, Giulio Soliani · Journal of Physics A Mathematical and Theoretical · 2007
We address the generalized measurement of the two-boson operator Z γ = a 1 + γ a † 2 which, for |γ| 2 ≠ 1, is not normal and cannot be detected by a joint measurement of quadratures on the two bosons. We explicitly construct the minimal Naimark extension, which involves a single additional bosonic system, and present its decomposition in terms of two-boson linear SU (2) interactions. The statistics of the measurement and the added noise are analysed in detail. Results are exploited to revisit the Caves–Shapiro concept of generalized phase observable based on heterodyne detection.