Trading quantum states for temporal profiles: tomography by the overlap

TL;DR

This paper introduces a method for quantum state and mode structure tomography using interference with a coherent probe and a single on/off detector, enabling efficient extraction of quantum information.

Contribution

The authors propose a novel scheme that trades quantum state knowledge for mode structure information and vice versa, using simple experimental setups with minimal detectors.

Findings

Experimental demonstration with a single control parameter

Complete tomography of the diagonal density matrix part

Feasible implementation with current optical technology

Abstract

Quantum states and the modes of the optical field they occupy are intrinsically connected. Here, we show that one can trade the knowledge of a quantum state to gain information about the underlying mode structure and, vice versa, the knowledge about the modal shape allows one to perform a complete tomography of the quantum state. Our scheme can be executed experimentally using the interference between the signal and probe states on an unbalanced beam splitter with a single on/off-type detector. By changing the temporal overlap between the signal and the probe, the imperfect interference is turned into a powerful tool to extract the information about the signal mode structure. A single on/off detector is already sufficient to collect the necessary measurement data for the reconstruction of the diagonal part of the density matrix of an arbitrary multi-mode signal. Moreover, we experimentally demonstrate the feasibility of our scheme with just one control parameter -- the time-delay of a coherent probe field.