Collapse-free action at a distance by multiple photon annihilations and tracking the action with a photon-number measurement

Abstract

The so-called quantum vampire effect, or, namely, collapse-free action at a distance by photon annihilation operator, is introduced in Optica 2, 112 (2015). Here, we investigate the quantum vampire effect in scenarios involving multiple photon annihilation on two different optical beams. We show that all $m$-time photon annihilations in some specific state will generate the same output, meaning that $m$ vampires can hide both their locations and their numbers in each optical mode. This demonstrates another interesting and strange phenomenon of quantum optics that originates from the property of the annihilation operator: $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}|0\ensuremath{\rangle}=0$. However, the annihilation operator is a nonphysical and nonunitary operation, and realistic implementation of photon annihilation is performed with the beam splitter and photon detector. We find that realistic photon annihilation will ``leave'' some shadow that makes the quantum vampire easier to track in real scenarios. We design a simple quantum measurement to catch realistic quantum vampires.