Direct tomography of high-dimensional density matrices for general quantum states of photons

TL;DR

This paper introduces a direct, high-dimensional quantum state tomography method using a polarization-resolving camera, enabling rapid, real-time measurement of photon density matrices up to 580x580 in size, independent of Hilbert space dimension.

Contribution

The authors develop a novel direct tomography protocol that allows for fast, parallel measurement of high-dimensional quantum states without increasing data acquisition time.

Findings

Successfully measured density matrices up to 580x580 dimensions.

Data acquisition time is independent of Hilbert space dimension, limited only by camera exposure.

Potential for real-time monitoring and high-dimensional quantum metrology.

Abstract

Quantum state tomography is the conventional method used to characterize density matrices for general quantum states. However, the data acquisition time generally scales linearly with the dimension of the Hilbert space, hindering the possibility of dynamic monitoring of a high-dimensional quantum system. Here, we demonstrate a direct tomography protocol to measure density matrices of photons in the position basis through the use of a polarization-resolving camera, where the dimension of density matrices can be as large as 580$\times$580 in our experiment. The use of the polarization-resolving camera enables parallel measurements in the position and polarization basis and as a result, the data acquisition time of our protocol does not increase with the dimension of the Hilbert space and is solely determined by the camera exposure time (on the order of 10 ms). Our method is potentially useful for the real-time monitoring of the dynamics of quantum states and paves the way for the development of high-dimensional, time-efficient quantum metrology techniques.