Reconstructing high-dimensional two-photon entangled states via compressive sensing
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 , 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.
Cite
@article{arxiv.1407.7426,
title = {Reconstructing high-dimensional two-photon entangled states via compressive sensing},
author = {Francesco Tonolini and Susan Chan and Megan Agnew and Alan Lindsay and Jonathan Leach},
journal= {arXiv preprint arXiv:1407.7426},
year = {2014}
}