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

• URL: http://arxiv.org/abs/2210.15585v2
• Date: Thu, 20 Apr 2023 15:06:34 GMT
• Title: Growing Schr\"odinger's cat states by local unitary time evolution of product states
• Authors: Saverio Bocini, Maurizio Fagotti
• Abstract summary: We show that, typically, a macroscopically-entangled state naturally grows after a single projective measurement of just one spin in the trivial eigenstate. We identify a condition under which what is growing is a "Schr"odinger's cat state"
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• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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