Quantum smoothing for classical mixtures

TL;DR

This paper explores quantum smoothing in superconducting qubits, demonstrating that smoothed probabilities do not always correspond to classical mixtures, challenging classical interpretations of quantum states at past times.

Contribution

It introduces experimental evidence showing smoothed probabilities in quantum systems can defy classical mixture interpretation, extending quantum smoothing theory.

Findings

Smoothed probabilities differ from classical mixture interpretations.

Experiments conducted on superconducting qubits.

Quantum smoothing reveals non-classical features in past state inference.

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 $\{|n\rangle\}$, it may be treated as a classical mixture, i.e., a system which randomly occupies the basis states $|n\rangle$ with probabilities $\rho_{nn}(t)$. Fully equivalent to so-called smoothing in classical probability theory, subsequent probing of the occupation of the states $|n\rangle$ 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 $t$.