Kavli Affiliate: Matthew P. A. Fisher
| First 5 Authors: Diego Barberena, Matthew P. A. Fisher, , ,
| Summary:
We study in detail the postselection problem in a specific model: bosons
hopping on a lattice subjected to continuous local measurements of quadrature
observables. We solve the model analytically and show that the postselection
overhead can be reduced by postprocessing the entire measurement record into
one or two numbers for each trajectory and then postselecting based only on
these numbers. We then provide a step-by-step protocol designed to recover
connected two-point functions of the quantum trajectories, which display an
exponentially decaying profile that is not observable in the unconditional,
trajectory averaged, state. With the analytical solution in hand, we analyse
the features of this postprocessing stage with the intention of abstracting
away the properties that make postselection feasible in this model and may help
in mitigating postselection in more general settings. We also test the protocol
numerically in a way that utilizes only experimentally accessible information,
showing that various quantum trajectory observables can be recovered with a few
repetitions of the numerical experiment, even after including inevitable
coarse-graining procedures expected under realistic experimental conditions.
Furthermore, all the information required to design the postprocessing stage is
independently present both in the unconditional dynamics and also in the
measurement record, thus bypassing the need to solve for the conditional
evolution of the model. We finalize by providing experimental implementations
of these models in cavity-QED and circuit-QED.
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