2024/12/06 by Swift, Carter, Nandini Trivedi, Trivedi, Nandini · 1 citation
Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Numerical methods in inverse problems #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.2412.05226
openalex publication_date 2024/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ⟨ A ⟩ 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.