Growing Schrödinger's cat states by local unitary time evolution of product states
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914887383384064 |
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| author | Bocini, Saverio Fagotti, Maurizio |
| author_facet | Bocini, Saverio Fagotti, Maurizio |
| contents | 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 "Schrödinger'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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_15585 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Growing Schrödinger's cat states by local unitary time evolution of product states Bocini, Saverio Fagotti, Maurizio Quantum Physics Statistical Mechanics Strongly Correlated Electrons 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 "Schrödinger'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. |
| title | Growing Schrödinger's cat states by local unitary time evolution of product states |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2210.15585 |