Fate of the area-law after partial measurement in quantum field theories

Abstract

We calculate numerically the Rényi bipartite entanglement entropy of the ground state of Klein-Gordon field theory (coupled harmonic oscillators) after fixing the position (partial measurement) of some of the oscillators in $d=1,2$ and $3$ dimensions. We show that after partial measurement as far as the two parts are connected the area-law is valid in generic dimensions except in $d=1$ conformal field theories. When due to the measured region the two parts are disconnected, the entanglement entropy decreases exponentially with respect to the minimum distance between the regions. In the massless case the decay is power-law with a universal dimension-dependent exponent.

9 pages, 11+2 figures! Part of this paper is replaced with a new article arXiv: 1512.03940 which has a new title and has much more details including fresh analytical results. The other half hopefully will appear in another future work!

Cited by in corpus (5)

• Holographic Pseudo Entropy
• Correlation functions of the CFTs on torus with $T\bar{T}$ deformation
• Post measurement bipartite entanglement entropy in conformal field theories
• On the Page curve under final state projection
• Entanglement entropy after selective measurements in quantum chains