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

Matteo G A Paris; Giulio Landolfi; Giulio Soliani

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

Matteo G A Paris·Giulio Landolfi·Giulio Soliani

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Abstract

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.

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Matteo G A Paris, Giulio Landolfi, Giulio Soliani. 2007-05-09. Generalized measurement of the non-normal two-boson operator $Z_γ= a_1 + γa_2^†$. https://arxiv.org/abs/quant-ph/0703093

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