TY - JOUR

T1 - How to Estimate Past Quantum Measurement Interventions After Continuous Monitoring

AU - Gough, John

N1 - Publisher Copyright:
© 2020, Pleiades Publishing, Ltd.

PY - 2020/5/31

Y1 - 2020/5/31

N2 - We analyze the problem of estimating past quantum states of a monitored system from a mathematical perspective in order to ensure self-consistency with the principle of quantum nondemolition. Despite several claims of “measuring noncommuting observables” in the physics literature, we show that we are always measuring commuting processes. Our main interest is in the notion of quantum smoothing, or retrodiction. In particular, we examine proposals to estimate the result of an external measurement made on an open quantum systems during a period where it is also undergoing continuous monitoring. A full analysis shows that the nondemolition principle is in place, and so a well-posed statistical inference problem can be formulated. We extend the formalism to consider multiple independent external measurements made on the system over the course of a continual period of monitoring.

AB - We analyze the problem of estimating past quantum states of a monitored system from a mathematical perspective in order to ensure self-consistency with the principle of quantum nondemolition. Despite several claims of “measuring noncommuting observables” in the physics literature, we show that we are always measuring commuting processes. Our main interest is in the notion of quantum smoothing, or retrodiction. In particular, we examine proposals to estimate the result of an external measurement made on an open quantum systems during a period where it is also undergoing continuous monitoring. A full analysis shows that the nondemolition principle is in place, and so a well-posed statistical inference problem can be formulated. We extend the formalism to consider multiple independent external measurements made on the system over the course of a continual period of monitoring.

UR - http://www.scopus.com/inward/record.url?scp=85085701462&partnerID=8YFLogxK

U2 - 10.1134/S1061920820020089

DO - 10.1134/S1061920820020089

M3 - Article

SN - 1061-9208

VL - 27

SP - 218

EP - 227

JO - Russian Journal of Mathematical Physics

JF - Russian Journal of Mathematical Physics

IS - 2

ER -