# Homodyne monitoring of post-selected decay

## TL;DR

This paper demonstrates how homodyne detection can monitor the decay of a superconducting qubit, revealing quantum trajectories, weak values, and state restrictions during post-selected decay processes.

## Contribution

It introduces experimental observation of quantum trajectories and weak values in superconducting qubits using homodyne detection, linking theory with experimental data.

## Key findings

- Conditional decay deviates from exponential law.
- Homodyne detection reveals anomalous weak values.
- Density matrix evolution is restricted to a specific surface.

## Abstract

We use homodyne detection to monitor the radiative decay of a superconducting qubit. According to the classical theory of conditional probabilities, the excited state population differs from an exponential decay law if it is conditioned upon a later projective qubit measurement. Quantum trajectory theory accounts for the expectation values of general observables, and we use experimental data to show how a homodyne detection signal is conditioned upon both the initial state and the finally projected state of a decaying qubit. We observe, in particular, how anomalous weak values occur in continuous weak measurement for certain pre- and post-selected states. Subject to homodyne detection, the density matrix evolves in a stochastic manner, but it is restricted to a specific surface in the Bloch sphere. We show that a similar restriction applies to the information associated with the post-selection, and thus bounds the predictions of the theory.