Eur. Phys. J. Special Topics 227, 365–378 (2018)
https://doi.org/10.1140/epjst/e2018-00086-8

Regular Article

Reducing backaction when measuring temporal correlations in quantum systems

¹ National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa
² Institute of Theoretical Physics, Department of Physics, University of Stellenbosch, Stellenbosch 7600, South Africa

^a e-mail: kastner@sun.ac.za

Received: 29 September 2017
Received in final form: 31 October 2017
Published online: 28 September 2018

Abstract

Dynamic correlations of quantum observables are challenging to measure due to measurement backaction incurred at early times. Recent work [P. Uhrich et al., Phys. Rev. A 96, 022127 (2017)] has shown that ancilla-based noninvasive measurements are able to reduce this backaction, allowing for dynamic correlations of single-site spin observables to be measured. We generalise this result to correlations of arbitrary spin observables and extend the measurement protocol to simultaneous noninvasive measurements which allow for real and imaginary parts of correlations to be extracted from a single set of measurements. We use positive operator-valued measures to analyse the dynamics generated by the ancilla-based measurements. Using this framework we prove that special observables exist for which measurement backaction is of no concern, so that dynamic correlations of these can be obtained without making use of ancillas.