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

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

2007-03-12

arxiv.org/abs/quant-ph/0703093v2

J. Phys. A: Math. Theor. 40 (2007) F531-F537.

Physics

Quantum Physics

8 pages, 2 figures, slightly revised version

Scientific paper

We address the generalized measurement of the two-boson operator $Z_\gamma= a_1 + \gamma a_2^\dag$ which, for $|\gamma|^2 \neq 1$, 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.

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