# Mainz 2017 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 31: Poster: Quantum Optics and Photonics I

### Q 31.63: Poster

### Dienstag, 7. März 2017, 17:00–19:00, P OG1+2

**Backwards Master Equation** — •Jonas Lammers^{1,2} and Klemens Hammerer^{1,2} — ^{1}Institut für Theoretische Physik, Leibniz Universität Hannover — ^{2}Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Leibniz Universität Hannover

The evolution of a quantum system undergoing continuous measurements is governed by the so-called conditional stochastic master equation. Using the past measurement record, it predicts the state of the system at a given time. We develop a method which allows to verify that state by *retrodiction*, using the future measurement record to compute the backwards evolution of the system.

We derive the stochastic backwards evolution equation of a quantum optical system using only basic quantum mechanics. The conditions on the system are very general so as to make the formalism applicable to a wide range of different setups. As an application, we examine how a Gaussian state evolves in a linear system, and compute the backwards equations of motion of its first and second moments. More concretely, we consider a one-dimensional harmonic oscillator under continuous position measurements coupled to a thermal bath. The proposed procedure allows to affirm the presence of desired properties such as entanglement or other non-classical features in a past quantum state, or even its whole density matrix.