Generalized measurement of the non-normal two-boson operator $Z_γ= a_1 + γa_2^†$

Paris, Matteo G A; Landolfi, Giulio; Soliani, Giulio

Generalized measurement of the non-normal two-boson operator $Z_γ= a_1 + γa_2^†$

Authors

Paris, Matteo G A

Landolfi, Giulio

Soliani, Giulio

Description

We address the generalized measurement of the two-boson operator $Z_γ= a_1 + γa_2^†$ which, for $|γ|^2 \neq 1$, 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 analyzed in details. Results are exploited to revisit the Caves-Shapiro concept of generalized phase observable based on heterodyne detection.
8 pages, 2 figures, slightly revised version