Quantum smoothing for classical mixtures

Abstract

In quantum mechanics, wave functions and density matrices represent our knowledge about a quantum system and give probabilities for the outcomes of measurements. If the combined dynamics and measurements on a system lead to a density matrix $\rho (t)$ with only diagonal elements in a given basis $\{|n⟩\}$, it may be treated as a classical mixture, i.e., a system which randomly occupies the basis states $|n⟩$ with probabilities ${\rho }_{nn}(t)$. Fully equivalent to so-called smoothing in classical probability theory, subsequent probing of the occupation of the states $|n⟩$ improves our ability to retrodict what was the outcome of a projective state measurement at time $t$. Here, we show with experiments on a superconducting qubit that the smoothed probabilities do not, in the same way as the diagonal elements of $\rho$, permit a classical mixture interpretation of the state of the system at the past time $t$.

5 pages, 4 figures

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• Weak values and the Leggett-Garg inequality in solid-state qubits
• Feedback control of a solid-state qubit using high-fidelity projective measurement
• Weak Values are Interference Phenomena
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Cited by in corpus (5)

• Prediction and retrodiction with continuously monitored Gaussian states
• Homodyne monitoring of post-selected decay
• Past observable dynamics of a continuously monitored qubit
• Smoothed quantum-classical states in time-irreversible hybrid dynamics
• Conditioned spin and charge dynamics of a single electron quantum dot