Efficient quantum tomography with incomplete measurement settings

Vladimír Bužek, G. Drobný, H. Wiedemann

Vladimír Bužek

Douglas Soares Gonçalves, Carlile Lavor, Márcia A. Gomes-Ruggiero +3 more

Whenever we do not have an informationally complete set of measurements, the estimate of a quantum state cannot be uniquely determined. In this case, among the density matrices compatible with the available data, the one commonly preferred is the one which is the most uncommitted to the missing information. This is the purpose of the maximum entropy estimation (MaxEnt) and the variational quantum tomography (VQT). Here, we propose a variant of VQT and show its relationship with MaxEnt methods in quantum tomographies with an incomplete set of measurements. We prove their equivalence in the case of eigenbasis measurements, and through numerical simulations we stress their similar behavior. Hence, in the modified VQT formulation we have an estimate of a quantum state as unbiased as in MaxEnt and with the benefit that VQT can be more efficiently solved by means of linear semidefinite programs.

Langford, Gilchrist, White +1 more

Areeya Chantasri, Shengshi Pang, Teerawat Chalermpusitarak +1 more

Hailan Ma, Daoyi Dong, Ian R. Petersen

Quantum state tomography is defined as a process of reconstructing the density matrix of a quantum state and is an important task for various emerging quantum technologies. In this work, we propose a general quantum state tomography framework that employs deep neural networks to reconstruct quantum states from a set of measurements with high efficiency. In particular, we apply it to two cases, including few measurement copies and incomplete measurement. Numerical results demonstrate that the proposed method exhibits a significant potential to achieve high fidelity for quantum state tomography when measurement resources are limited.