title: 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 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.
authors.affiliation: SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK.
authors.forename: Francesco
authors.initials: F
authors.lastname: Tonolini
authors.affiliation: SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK.
authors.forename: Susan
authors.initials: S
authors.lastname: Chan
authors.affiliation: SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK.
authors.forename: Megan
authors.initials: M
authors.lastname: Agnew
authors.affiliation: 1] SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK [2] Applied and Computational Mathematics and Statistics, University of Notre Dame, USA.
authors.forename: Alan
authors.initials: A
authors.lastname: Lindsay
authors.affiliation: SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Leach