Quantum trajectory simulation of weak measurements with post-selection

Areeya Chantasri, Justin Dressel, Steven J. Weber +3 more

Jeff Tollaksen, Andrei Yu. Khrennikov, Gregg S. Jaeger +2 more

Jeff Tollaksen

Antti P. Vepsäläinen

The concept of weak value of a quantum mechanical observable is based on a weak measurement followed by a strong measurement of a complementary observable. By applying post-selection, the weak value can, under certain circumstances, have values much higher than would be possible without post-selection, even above the highest eigenvalue of the measurement operator. Weak values have a wide range of applications, starting from the amplification of the resolution in high sensitivity metrology. The weak values have been especially successful in the area of quantum optics, which provides a suitable set of tools for performing the weak measurements with post-selection. The topic of this thesis is to lay the ground for the adaptation of weak values also in other fields of physics, the target being to harness the weak values in cavity quantum electrodynamics (cQED), and furthermore in circuit quantum electrodynamics. The main complication in the adaptation in these fields is the de-coherence, which is almost nonexistent in quantum optics. In this thesis we use quantum trajectory simulation to model the weak values under experimentally realistic conditions. We show how the weak values stem from the stochastic description of the quantum mechanical measurement, and that the second order approximation of the weak values is not sufficient in describing the effects of the measurement strength on the weak values. Using the simulation we demonstrate that the measurement resolution can be increased by applying post-selection even in the presence of de-coherence. Finally, we study the correlations between two entangled qubit, and show that post-selection appears to strengthen it.

Anirban Ch Narayan Chowdhury

Zhang, Miao

Due to the reduced probability of successful post-selection, the weak-value amplification seems to be unavailable for the parameter-estimation. Here, we show theoretically that, some effects due to the weak interactions present only in the properly post-selected sub-ensemble, however are canceled by themselves in the total ensemble. From this point of view, the post-selection induced weak value could be one of the feasible methods for measuring the weak interaction, since the standard measurement does not work. Additionally, we employ the system of trapped ions to simulate the weak measurement and calculate relevant results without the frequently-used weak interaction approximation.