Homodyne monitoring of post-selected decay

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.

11 pages, 8 figures

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Cited by in corpus (10)

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• Pontryagin-Optimal Control of a non-Hermitian Qubit
• Quantum retrodiction in Gaussian systems and applications in optomechanics
• Retrodiction of measurement outcomes on a single quantum system reveals entanglement with its environment
• Continuous monitoring measured signals bounded by past and future conditions in enlarged quantum systems
• Homodyne Measurement of a Non-Hermitian Qubit Undergoing Fluorescence