Post-selection and quantum energetics
- URL: http://arxiv.org/abs/2207.14194v1
- Date: Thu, 28 Jul 2022 15:59:38 GMT
- Title: Post-selection and quantum energetics
- Authors: Spencer Rogers, Andrew N. Jordan
- Abstract summary: We investigate the anomalous energy change of the measurement apparatus when a qubit is measured in bases that do not commute with energy.
We model two possible measurement implementations: one is a quantum clock model with a completely time-independent Hamiltonian, while the other is a Jaynes-Cummings model which is time-dependent but conserves the total excitation number.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We investigate the anomalous energy change of the measurement apparatus when
a qubit is measured in bases that do not commute with energy. We model two
possible measurement implementations: one is a quantum clock model with a
completely time-independent Hamiltonian, while the other is a Jaynes-Cummings
model which is time-dependent but conserves the total excitation number. We
look at the mean energy change of the measurement apparatus in both models,
conditioned on the qubit post-selection, and find that this change can be much
greater than the level spacing of the qubit, like an anomalous weak value. In
the clock model, the expression for the apparatus energy shift explicitly
contains the weak value of the qubit Hamiltonian. However, in our case, no
explicit weak measurements are carried out. Our two models give different
results, which we explain to be a consequence of the non-degenerate spectrum of
the Jaynes-Cummings model. We compare our calculations in the Jaynes-Cummings
model with the experimental data of [J. Stevens, et al, arXiv:2109.09648
(2021)] and find good agreement when the conditions of our derivation are
valid.
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