Cat state, sub-Planck structure and weak measurement

TL;DR

This paper explores the relationship between Heisenberg-limited and weak measurements using quantum cat states with sub-Planck structures, revealing their complementary regimes based on state overlap.

Contribution

It establishes a connection between sub-Planck structures in cat states and the regimes of weak measurement phenomena, highlighting their complementary nature.

Findings

Sub-Planck structure obscures imaginary weak values.

Weak measurement effects depend on the overlap of mesoscopic states.

The phenomena manifest in distinct, non-overlapping regimes.

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.