Post-selection and quantum energetics

TL;DR

This paper explores the unexpected energy changes in measurement devices during qubit measurements in non-energy bases, using two models, and compares theoretical predictions with experimental data, revealing insights into quantum energetics and weak values.

Contribution

It introduces two models for measurement-induced energy changes in qubits, linking them to weak values without explicit weak measurements, and compares theoretical results with experimental data.

Findings

Apparent energy shifts can exceed qubit level spacing.

The clock model explicitly involves weak values in energy shifts.

Results align well with experimental data under certain conditions.

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.