Generalized measurement of the non-normal two-boson operator $Z_\gamma = a_1 + \gamma a_2^\dag$

Matteo G A Paris; Giulio Landolfi; Giulio Soliani

Generalized measurement of the non-normal two-boson operator $Z_\gamma = a_1 + \gamma a_2^\dag$

Quantum Physics 2007-06-12 v2

Authors: Matteo G A Paris , Giulio Landolfi , Giulio Soliani

Abstract

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.

Keywords

generalized measurement non-normal operator two-boson operator naimark extension su(2) interactions heterodyne detection

Cite

@article{arxiv.quant-ph/0703093,
  title  = {Generalized measurement of the non-normal two-boson operator $Z_\gamma = a_1 + \gamma a_2^\dag$},
  author = {Matteo G A Paris and Giulio Landolfi and Giulio Soliani},
  journal= {arXiv preprint arXiv:quant-ph/0703093},
  year   = {2007}
}

Comments

8 pages, 2 figures, slightly revised version

Generalized measurement of the non-normal two-boson operator $Z_\gamma = a_1 + \gamma a_2^\dag$

Abstract

Keywords

Cite

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