2016/09/30 by Jun-Yi Wu, Holger F. Hofmann · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Bipartite graph #Discrete mathematics #Mathematics #Multipartite entanglement #Neural Networks and Reservoir Computing #Observable #Photon #Photon entanglement #Physics #Quantum #Quantum Information and Cryptography #Quantum entanglement #Quantum mechanics #Quantum optics #Squashed entanglement #Statistical physics #quant-ph
paper · pdf · doi:10.1088/1367-2630/aa87ad
published as New J. Phys. 19 103032, 2017 · 26 pages, 4 figures; This is the published version with the amended introduction, explanations of equations and conclusion
openalex publication_date 2017/08/22 · arxiv created 2017/10/27 · arxiv updated 2017/10/30 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/06
Optical multi-mode systems provide large scale Hilbert spaces that can be accessed and controlled using single photon sources, linear optics and photon detection. Here, we consider the bipartite entanglement generated by coherently distributing M photons in M modes to two separate locations, where linear optics and photon detection is used to verify the non-classical correlations between the two M -mode systems. We show that the entangled state is symmetric under mode shift operations performed in the two systems and use this symmetry to derive correlations between photon number distributions detected after a discrete Fourier transform (DFT) of the modes. The experimentally observable correlations can be explained by a simple and intuitive rule that relates the sum of the output mode indices to the eigenvalue of the input state under the mode shift operation. Since the photon number operators after the DFT do not commute with the initial photon number operators, entanglement is necessary to achieve strong correlations in both the initial mode photon numbers and the photon numbers observed after the DFT. We can therefore derive entanglement witnesses based on the experimentally observable correlations in both photon number distributions, providing a practical criterion for the evaluation of large scale entanglement in optical multi-mode systems. Our method thus demonstrates how non-classical signatures in large scale optical quantum circuits can be accessed experimentally by choosing an appropriate combination of modes in which to detect the photon number distributions that characterize the quantum coherences of the state.