Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2412.05226 |
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Sommario:
- 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.