1National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093 2Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 3Key Laboratory of Weak-Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin 300071
Abstract：High-dimensional (HD) entanglement provides a very promising way of transcending the limitations of the two-dimensional entanglement between qubits for increasing channel capacity in many quantum protocols. In the pursuit of capitalizing on the HD entangled states, one of the central issues is to unambiguously and comprehensively quantify and reconstruct them. The full quantum state tomography is a unique solution, but it is undesirable and even impractical because the measurements increase rapidly in $d^4$ for a bipartite $d$-dimensional quantum state. Here we present a very efficient and practical tomography method—asymptotical locking tomography (ALT), which can harvest full information of bipartite $d$-dimensional entangled states by very few measurements less than $2d^2$ only. To showcase the validity and reasonableness of our ALT, we carry out the test with the two-photon spin-orbital angular momentum hyperentangled states in a four-dimensional subspace. Besides high-efficiency and practicality, our ALT is also universal and can be generalized into multipartite HD entanglement and other quantum systems.
Wang X L, Chen L K, Li W, Huang H L, Liu C, Chen C, Luo Y H, Su Z E, Wu D, Li Z D, Lu H, Hu Y, Jiang X, Peng C Z, Li L, Liu N L, Chen Y A, Lu C Y and Pan J W 2016 Phys. Rev. Lett.117 210502
Kelly J, Barends R, Fowler A G, Megrant A, Jeffrey E, White T C, Sank D, Mutus J Y, Campbell B, Chen Y, Chen Z, Chiaro B, Dunsworth A, Hoi I C, Neill C, O'Malley P J J, Quintana C, Roushan P, Vainsencher A, Wenner J, Cleland A N and Martinis J M 2015 Nature519 66
Wang J, Paesani S, Ding Y, Santagati R, Skrzypczyk P, Salavrakos A, Tura J, Augusiak R, Mančinska L, Bacco D, Bonneau D, Silverstone J W, Gong Q H, Acín A, Rottwitt K, Oxenløwe L K, O'Brien J L, Laing A and Thompson M G 2018 Science360 285
2020, Vol. 37 
