Objective Compressive Quantum Process Tomography

TL;DR

This paper introduces a compressive quantum process tomography method that efficiently characterizes rank-deficient quantum processes using random inputs and adaptive measurements, suitable for many-body quantum systems.

Contribution

It presents a novel, assumption-free scheme combining certification and compressive reconstruction, applicable to entangled and tensor-product configurations in quantum process tomography.

Findings

Efficient reconstruction of quantum processes with minimal measurement resources.

Compatible with multipartite quantum systems and various input states.

Demonstrated effectiveness through simulations with optical systems.

Abstract

We present a compressive quantum process tomography scheme that fully characterizes any rank-deficient completely-positive process with no a priori information about the process apart from the dimension of the system on which the process acts. It uses randomly-chosen input states and adaptive output von Neumann measurements. Both entangled and tensor-product configurations are flexibly employable in our scheme, the latter which naturally makes it especially compatible with many-body quantum computing. Two main features of this scheme are the certification protocol that verifies whether the accumulated data uniquely characterize the quantum process, and a compressive reconstruction method for the output states. We emulate multipartite scenarios with high-order electromagnetic transverse modes and optical fibers to positively demonstrate that, in terms of measurement resources, our assumption-free compressive strategy can reconstruct quantum processes almost equally efficiently using all types of input states and basis measurement operations, operations, independent of whether or not they are factorizable into tensor-product states.