Eliska Greplova, Christian Kraglund Andersen, Klaus Mølmer: **Quantum parameter estimation with a neural network**, arXiv:1711.05238

We propose to use neural networks to estimate the rates of coherent and incoherent processes in quantum systems from continuous measurement records. In particular, we adapt an image recognition algorithm to recognize the patterns in experimental signals and link them to physical quantities. We demonstrate that the parameter estimation works unabatedly in the presence of detector imperfections which complicate or rule out Bayesian filter analyses.

Eliska Greplova, Edward E. Laird, G. Andrew D. Briggs, Klaus Mølmer: **Conditioned spin and charge dynamics of a single electron quantum dot**, Physical Review A 96, 052104 (2017) (Editors’ Suggestion), arXiv:1708:06680

In this article we describe the incoherent and coherent spin and charge dynamics of a single electron quantum dot. We use a stochastic master equation to model the state of the system, as inferred by an observer with access to only the measurement signal. Measurements obtained during an interval of time contribute, by a past quantum state analysis, to our knowledge about the system at any time t within that interval. Such analysis permits precise estimation of physical parameters, and we propose and test a modification of the classical Baum-Welch parameter re-estimation method to systems driven by both coherent and incoherent processes.

Eliska Greplova, Klaus Mølmer, Christian Kraglund Andersen: **Quantum teleportation with continuous measurements**, Physical Review A 94, 042334 (2016), arXiv:1608:01814

We propose a scheme for quantum teleportation between two qubits, coupled sequentially to a cavity field. An implementation of the scheme is analyzed with superconducting qubits and a transmission line resonator, where measurements are restricted to continuous probing of the field leaking from the resonator rather than instantaneous projective Bell state measurement. We show that the past quantum state formalism [S. Gammelmark et al, Phys. Rev. 111, 160401] can be successfully applied to estimate what would have been the most likely Bell measurement outcome conditioned on our continuous signal record. This information determines which local operation on the target qubit yields the optimal teleportation fidelity. Our results emphasize the significance of applying a detailed analysis of quantum measurements in feed-forward protocols in non-ideal leaky quantum systems.

Qing Xu, Eliska Greplova, Brian Julsgaard, Klaus Mølmer: **Correlation functions and conditioned quantum dynamics in photodetection theory**, Physica Scripta 90, 128004 (2015) (Invited Comment), arXiv:1506:08654

Correlations in photodetection signals from quantum light sources are conventionally calculated by application of the source master equation and the quantum regression theorem. In this article we show how the conditioned dynamics, associated with the quantum theory of measurements, allows calculations and offers interpretations of the behaviour of the same quantities. Our theory is illustrated for photon counting and field-amplitude measurements, and we show, in particular, how transient correlations between field-amplitude measurements and later photon counting events can be accounted for by a recently developed theory of past quantum states of a monitored quantum system.

Eliska Greplova, Geza Giedke: **Degradability of Fermionic Gaussian Channels**, Physical Review Letters 121, 200501 (2018), arXiv:160401954

We study the degradability of fermionic Gaussian channels. Fermionic quantum channels are a central building block of quantum information processing with fermions and the family of Gaussian channels, in particular, is relevant in the emerging field of electron quantum optics and its applications for quantum information. Degradable channels are of particular interest since they have additive quantum capacity. We derive a simple standard form for fermionic Gaussian channels. This allows us fully characterize all degradable n-mode fermionic Gaussian channels. Consequences for the quantum capacity of those channels are discussed.