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| Format: | Preprint |
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2024
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| Online-Zugang: | https://arxiv.org/abs/2412.05226 |
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| _version_ | 1866909601571536896 |
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| author | Swift, Carter Trivedi, Nandini |
| author_facet | Swift, Carter Trivedi, Nandini |
| contents | Two hallmarks of quantum non-demolition (QND) measurement are the ensemble-level conservation of the expectation value of the measured observable $A$ and the eventual, inevitable collapse of the system into some eigenstate of $A$. This requires that $A$ commutes with $H$, the system's Hamiltonian. In what we term "Auxiliary Observable QND" measurement, $A$ does not commute with $H$ and the above two characteristics clearly cannot be present as the system's dynamics prevent $\langle A \rangle$ from reaching a definite value. However, in this paper we find that under such a measurement QND behavior still arises, but is seen in the behavior of a secondary "target" observable we call $B$, with the condition that $B$ commutes with both $A$ and $H$. In such cases, the expectation value of $B$ is conserved and the system at least partially collapses with respect to eigenstates of $B$. We show as an example how this surprising result applies to a Heisenberg chain, where we demonstrate that local measurements on a single site can reveal information about the spectrum of an entire system, a finding which may be of practical use in experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial Wavefunction Collapse Under Repeated Weak Measurement of a non-Conserved Observable Swift, Carter Trivedi, Nandini Quantum Physics Two hallmarks of quantum non-demolition (QND) measurement are the ensemble-level conservation of the expectation value of the measured observable $A$ and the eventual, inevitable collapse of the system into some eigenstate of $A$. This requires that $A$ commutes with $H$, the system's Hamiltonian. In what we term "Auxiliary Observable QND" measurement, $A$ does not commute with $H$ and the above two characteristics clearly cannot be present as the system's dynamics prevent $\langle A \rangle$ from reaching a definite value. However, in this paper we find that under such a measurement QND behavior still arises, but is seen in the behavior of a secondary "target" observable we call $B$, with the condition that $B$ commutes with both $A$ and $H$. In such cases, the expectation value of $B$ is conserved and the system at least partially collapses with respect to eigenstates of $B$. We show as an example how this surprising result applies to a Heisenberg chain, where we demonstrate that local measurements on a single site can reveal information about the spectrum of an entire system, a finding which may be of practical use in experiments. |
| title | Partial Wavefunction Collapse Under Repeated Weak Measurement of a non-Conserved Observable |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2412.05226 |