Physical currents for stochastic Einstein-Podolsky-Rosen quantum trajectories

TL;DR

This paper simulates the measured homodyne current in EPR correlations, showing that Stratonovich noise aligns with experiments and highlighting implications for quantum measurement noise and errors.

Contribution

It identifies the correct stochastic noise model for EPR measurements and proposes a modernized Schrödinger's thought experiment involving simultaneous position and momentum measurements.

Findings

Stratonovich noise matches experimental data.

Simulation clarifies measurement noise in quantum technologies.

Proposes a new version of Schrödinger's thought experiment.

Abstract

Theories of the measured homodyne current generated by a stochastic Schr\"odinger equation (SSE) can be tested in a simulation of the Einstein-Podolsky-Rosen (EPR) correlations for a two-mode squeezed state. We carry out such a simulation, and determine the correct stochastic term for the measured current in the broad-band limit. Stratonovich rather than Ito stochastic noise agrees with experiment. We show that this is relevant to measurement noise and errors in quantum technologies. By analyzing the SSE trajectories as measurement settings are changed, we propose a modern version of Schrodinger's gedanken experiment, where one measures position and momenta simultaneously, ``one by direct, the other by indirect measurement''.