Enhancing multi-step quantum state tomography by PhaseLift

Yiping Lu, Huan Liu, Qing Bo Zhao

A Jenefa, Edward Naveen VijayaKumar, Manoranjitham Rajendran +5 more

Yiping Lu, Qing Bo Zhao

Multi-photon system has been studied by many groups. The challenge facing by most groups is the limited samples are far from enough for detecting quantum entanglement. The problem is even more serious for the quantum state tomography. Adaptive quantum state tomography is one possible way to solve the problem. We develop a distribution scheme of samples and extend it into three step to improve the performance of adaptive quantum state tomography. Mean Square Error of reconstructed density matrix is improved for several states being tested numerically. In addition, Phaselift is applied to save the storage space of measurement operator.

Gregory S. Kanter, Prem Kumar

Yi-Kai Liu, Shelby Kimmel

We develop a method for quantum process tomography that combines the efficiency of compressed sensing with the robustness of randomized benchmarking. Our method is robust to state preparation and measurement errors, and it achieves a quadratic speedup over conventional tomography when the unknown process is a generic unitary evolution. Our method is based on PhaseLift, a convex programming technique for phase retrieval. We show that this method achieves approximate recovery of almost all signals, using measurements sampled from spherical or unitary 2-designs. This is the first positive result on PhaseLift using 2-designs. We also show that exact recovery of all signals is possible using unitary 4-designs. Previous positive results for PhaseLift required spherical 4-designs, while PhaseLift was known to fail in certain cases when using spherical 2-designs.

M. Cramer, Martin Bodo Plenio, Steven T. Flammia +6 more