Eur. Phys. J. D (2013) 67: 182
https://doi.org/10.1140/epjd/e2013-30592-9

Regular Article

Cat state, sub-Planck structure and weak measurement

¹ Graduate School of Information Science, Nagoya University, Chikusa-ku, 464-8601 Nagoya, Japan
² Indian Institute of Science Education and Research Kolkata, Mohanpur, 741252 Nadia, India

^a e-mail: akp@math.cm.is.nagoya-u.ac.jp
^b e-mail: pprasanta@iiserkol.ac.in

Received: 25 September 2012
Received in final form: 22 April 2013
Published online: 19 August 2013

Abstract

Heisenberg-limited and weak measurements are the two intriguing notions, used in recent times for enhancing the sensitivity of measurements in quantum metrology. Using a quantum cat state, endowed with sub-Planck structure, we connect these two novel concepts. It is demonstrated that these two phenomena manifest in complementary regimes, depending upon the degree of overlap between the mesoscopic states constituting the cat state under consideration. In particular, we find that when sub-Planck structure manifests, the imaginary weak value is obscured and vice versa.