Complete Quantum-State Tomography with a Local Random Field

TL;DR

This paper demonstrates that complete quantum-state tomography of a multi-qubit system can be achieved by controlling a single qubit with a local random pulse, validated experimentally with high fidelity in a nitrogen-vacancy center.

Contribution

It introduces a method for quantum-state tomography using only local random control on a single qubit, simplifying the process for complex quantum systems.

Findings

Achieved >95% fidelity in reconstructing entangled states

Validated the method experimentally on NV centers in diamond

Outlined potential for characterizing unknown quantum processes

Abstract

Single-qubit measurements are typically insufficient for inferring arbitrary quantum states of a multi-qubit system. We show that if the system can be fully controlled by driving a single qubit, then utilizing a local random pulse is almost always sufficient for complete quantum-state tomography. Experimental demonstrations of this principle are presented using a nitrogen-vacancy (NV) center in diamond coupled to a nuclear spin, which is not directly accessible. We report the reconstruction of a highly entangled state between the electron and nuclear spin with fidelity above 95%, by randomly driving and measuring the NV-center electron spin only. Beyond quantum-state tomography, we outline how this principle can be leveraged to characterize and control quantum processes in cases where the system model is not known.