Growing Schr\"odinger's cat states by local unitary time evolution of product states

TL;DR

This paper demonstrates that in quantum spin-chain systems, a single local measurement can induce the formation of macroscopic entangled states, including Schr"odinger's cat states, under generic conditions without special entanglement requirements.

Contribution

It identifies conditions under which local measurements lead to the natural growth of macroscopic entangled states, including Schr"odinger's cat states, in quantum many-body systems.

Findings

A single projective measurement can generate macroscopic entanglement.

Schr"odinger's cat states can form without special initial entanglement.

The results apply to systems with generic Hamiltonians and hidden symmetries.

Abstract

We envisage many-body systems that can be described by quantum spin-chain Hamiltonians with a trivial separable eigenstate. For generic Hamiltonians, such a state represents a quantum scar. We show that, typically, a macroscopically-entangled state naturally grows after a single projective measurement of just one spin in the trivial eigenstate; moreover, we identify a condition under which what is growing is a "Schr\"odinger's cat state". Our analysis does not reveal any particular requirement for the entangled state to develop, provided that the trivial eigenstate does not minimise/maximise a local conservation law. We study two examples explicitly: systems described by generic Hamiltonians and a model that exhibits a $U(1)$ hidden symmetry. The latter can be reinterpreted as a 2-leg ladder in which the interactions along the legs are controlled by the local state on the other leg through transistor-like building blocks.