Instantaneous measurement can isolate the information

TL;DR

This paper demonstrates that under specific conditions, an instantaneous measurement on one end of a spin chain cannot influence the other end, effectively isolating the information of the measurement from the rest of the system.

Contribution

It shows that with an instantaneous measurement and an appropriately chosen initial state, the measurement's effect remains localized and does not propagate through the spin chain.

Findings

Instantaneous measurement effect remains localized under certain conditions.

The effect of measurement on the far end of the chain does not reach the initial point.

Information of the measurement is effectively isolated from the rest of the system.

Abstract

Consider a one-dimensional spin chain, from spin 1 to spin N, such that each spin interacts with its nearest neighbors. Performing a local operation (measurement) on spin N, we expect from the Lieb-Robinson velocity that, in general, the effect of this measurement achieves spin 1 after some while. But, in this paper, we show that if a) the measurement on spin N is performed instantaneously and b) the initial state of the spin chain is chosen appropriately, then the effect of the measurement on spin N never achieves spin 1. In other words, performing or not performing an instantaneous measurement on spin N at t=0 does not alter the reduced dynamics of spin 1 for all the times t>0. We can interpret this as the following: The information of performing an instantaneous measurement on spin N is isolated such that it cannot achieve spin 1.