Classifying two-body Hamiltonians for Quantum Darwinism
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909845163081728 |
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| author | Doucet, Emery Deffner, Sebastian |
| author_facet | Doucet, Emery Deffner, Sebastian |
| contents | Quantum Darwinism is a paradigm to understand how classically objective reality emerges from within a fundamentally quantum universe. Despite the growing attention that this field of research as been enjoying, it is currently not known what specific properties a given Hamiltonian describing a generic quantum system must have to allow the emergence of classicality. Therefore, in the present work, we consider a broadly applicable generic model of an arbitrary finite-dimensional system interacting with an environment formed from an arbitrary collection of finite-dimensional degrees of freedom via an unspecified, potentially time-dependent Hamiltonian containing at most two-body interaction terms. We show that such models support quantum Darwinism if the set of operators acting on the system which enter the Hamiltonian satisfy a set of commutation relations with a pointer observable and with one other. We demonstrate our results by analyzing a wide range of example systems: a qutrit interacting with a qubit environment, a qubit-qubit model with interactions alternating in time, and a series of collision models including a minimal model of a quantum Maxwell demon. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_00805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classifying two-body Hamiltonians for Quantum Darwinism Doucet, Emery Deffner, Sebastian Quantum Physics Statistical Mechanics Quantum Darwinism is a paradigm to understand how classically objective reality emerges from within a fundamentally quantum universe. Despite the growing attention that this field of research as been enjoying, it is currently not known what specific properties a given Hamiltonian describing a generic quantum system must have to allow the emergence of classicality. Therefore, in the present work, we consider a broadly applicable generic model of an arbitrary finite-dimensional system interacting with an environment formed from an arbitrary collection of finite-dimensional degrees of freedom via an unspecified, potentially time-dependent Hamiltonian containing at most two-body interaction terms. We show that such models support quantum Darwinism if the set of operators acting on the system which enter the Hamiltonian satisfy a set of commutation relations with a pointer observable and with one other. We demonstrate our results by analyzing a wide range of example systems: a qutrit interacting with a qubit environment, a qubit-qubit model with interactions alternating in time, and a series of collision models including a minimal model of a quantum Maxwell demon. |
| title | Classifying two-body Hamiltonians for Quantum Darwinism |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2405.00805 |