No-cost Bell nonlocality certification from quantum tomography and its applications in quantum-magic-resource witnessing

TL;DR

This paper demonstrates that standard Pauli-basis measurements used in quantum tomography can directly certify quantum nonlocality and magic without additional experimental effort, unifying state characterization and fundamental tests.

Contribution

It introduces a method to derive Bell inequalities from tomographic data, enabling nonlocality certification and quantum magic witnessing using only Pauli measurements.

Findings

Pauli measurements suffice for nonlocality certification from tomographic data

New Bell inequalities tailored to experimental scenarios are constructed

The approach unifies quantum state tomography with nonlocality and magic witnessing

Abstract

Tomographic measurements are the standard tool for characterizing quantum states, yet they are usually regarded only as means for state reconstruction or fidelity measurement. Here, we show that the same Pauli-basis measurements (X, Y, Z) can be directly employed for the certification of nonlocality at no additional experimental cost. Our framework allows any tomographic data - including archival datasets -- to be reinterpreted in terms of fundamental nonlocality tests. We introduce a generic, constructive method to generate tailored Bell inequalities and showcase their applicability to certify the non-locality of states in realistic experimental scenarios. Recognizing the stabilizer nature of the considered operators, we analyze our inequalities in the context of witnessing quantum magic - a crucial resource for quantum computing. Our approach requires Pauli measurements only and tests the quantum magic solely through the resources present in the state. Our results establish a universal standard that unifies state tomography with nonlocality certification and its application to quantum magic witnessing, thereby streamlining both fundamental studies and practical applications.