Reconstructing high-dimensional two-photon entangled states via compressive sensing

TL;DR

This paper demonstrates that compressive sensing can efficiently reconstruct high-dimensional two-photon entangled states with significantly fewer measurements than traditional methods, enabling faster and more practical quantum state characterization.

Contribution

The authors develop a modified compressive sensing algorithm incorporating singular value thresholding for efficient quantum state reconstruction of large-scale entangled systems.

Findings

Accurate reconstruction of a 17-dimensional two-photon entangled state with only 3% of measurements.

Reconstruction algorithm is fast, computationally inexpensive, and broadly applicable.

Method reduces measurement requirements from over 83,000 to about 2,500.

Abstract

Accurately establishing the state of large-scale quantum systems is an important tool in quantum information science; however, the large number of unknown parameters hinders the rapid characterisation of such states, and reconstruction procedures can become prohibitively time-consuming. Compressive sensing, a procedure for solving inverse problems by incorporating prior knowledge about the form of the solution, provides an attractive alternative to the problem of high-dimensional quantum state characterisation. Using a modified version of compressive sensing that incorporates the principles of singular value thresholding, we reconstruct the density matrix of a high-dimensional two-photon entangled system. The dimension of each photon is equal to $d= 17$, corresponding to a system of 83521 unknown real parameters. Accurate reconstruction is achieved with approximately 2500 measurements, only 3\% of the total number of unknown parameters in the state. The algorithm we develop is fast, computationally inexpensive, and applicable to a wide range of quantum states, thus demonstrating compressive sensing as an effective technique for measuring the state of large-scale quantum systems.