Past Quantum States of a Monitored System

Søren Gammelmark, Brian Julsgaard, and Klaus Mølmer
Phys. Rev. Lett. 111, 160401 – Published 15 October 2013
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Abstract

A density matrix ρ(t) yields probabilistic information about the outcome of measurements on a quantum system. We introduce here the past quantum state, which, at time T, accounts for the state of a quantum system at earlier times t<T. The past quantum state Ξ(t) is composed of two objects, ρ(t) and E(t), conditioned on the dynamics and the probing of the system until t and in the time interval [t, T], respectively. The past quantum state is characterized by its ability to make better predictions for the unknown outcome of any measurement at t than the conventional quantum state at that time. On the one hand, our formalism shows how smoothing procedures for estimation of past classical signals by a quantum probe [M. Tsang, Phys. Rev. Lett. 102, 250403 (2009)] apply also to describe the past state of the quantum system itself. On the other hand, it generalizes theories of pre- and postselected quantum states [Y. Aharonov and L. Vaidman, J. Phys. A 24, 2315 (1991)] to systems subject to any quantum measurement scenario, any coherent evolution, and any Markovian dissipation processes.

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  • Received 3 May 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.160401

© 2013 American Physical Society

Authors & Affiliations

Søren Gammelmark, Brian Julsgaard, and Klaus Mølmer*

  • Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark

  • *moelmer@phys.au.dk

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Issue

Vol. 111, Iss. 16 — 18 October 2013

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