Quantum State Smoothing Cannot Be Assumed Classical Even When the Filtering and Retrofiltering Are Classical

作     者：Kiarn T. Laverick Prahlad Warszawski Areeya Chantasri Howard M. Wiseman 

作者机构：Centre for Quantum Computation and Communication Technology (Australian Research Council) Centre for Quantum Dynamics Griffith University Yuggera Country Brisbane Queensland 4111 Australia Centre of Excellence in Engineered Quantum Systems (Australian Research Council) School of Physics The University of Sydney Gadigal Country Sydney New South Wales 2006 Australia Optical and Quantum Physics Laboratory Department of Physics Faculty of Science Mahidol University Bangkok 10140 Thailand Institute for Quantum Studies Chapman University Orange California 92866 USA 

出 版 物：《PRX Quantum》 (PRX. Quantum.)

年 卷 期：2023年第4卷第4期

页      面：040340-040340页

核心收录：

基　　金：NSRF of Thailand, (B05F650024) Australian Research Council, ARC, (CE170100012) Australian Research Council, ARC 

主　　题：Open quantum systems & decoherence Quantum feedback Quantum measurements Quantum stochastic processes 

摘      要：State smoothing is a technique to estimate a state at a particular time, conditioned on information obtained both before (past) and after (future) that time. For a classical system, the smoothed state is a normalized product of the filtered state (a state conditioned only on the past measurement information and the initial preparation) and the retrofiltered effect (depending only on the future measurement information). For the quantum case, while there are well-established analogues of the filtered state (ρF) and the retrofiltered effect (E^R), their product does not, in general, provide a valid quantum state for smoothing. However, this procedure does seem to work when ρF and E^R are mutually diagonalizable. This fact has been used to obtain smoothed quantum states—purer than the filtered states—in a number of experiments on continuously monitored quantum systems, in cavity QED and atomic systems. In this paper we show that there is an implicit assumption underlying this technique: that if all the information were known to the observer, the true system state would be one of the diagonal basis states. This assumption does not necessarily hold, as the missing information is quantum information. It could be known to the observer only if it were turned into a classical measurement record, but then its nature would depend on the choice of measurement. We show by a simple model that, depending on that measurement choice, the smoothed quantum state can: agree with that from the classical method, disagree with it but still be co-diagonal with it, or not even be co-diagonal with it. That is, just because filtering and retrofiltering appear classical does not mean classical smoothing theory is applicable in quantum experiments.