Testing Bell inequalities with circuit QEDs by joint spectral measurements

TL;DR

This paper proposes a practical method to test Bell's inequality using circuit QED systems by employing joint spectral measurements of two superconducting qubits, enabling direct observation of quantum nonlocality without full state tomography.

Contribution

It introduces a novel approach to verify Bell's inequality through joint spectral measurements in circuit QED, simplifying the experimental process and avoiding standard quantum state tomography.

Findings

Bell states can be confirmed without tomography

Bell's inequality can be tested via spectral measurements

Method is robust against experimental challenges

Abstract

We propose a feasible approach to test Bell's inequality with the experimentally-demonstrated circuit QED system, consisting of two well-separated superconducting charge qubits (SCQs) dispersively coupled to a common one-dimensional transmission line resonator (TLR). Our proposal is based on the joint spectral measurements of the two SCQs, i.e., their quantum states in the computational basis $\{|kl>,\,k,l=0,1\}$ can be measured by detecting the transmission spectra of the driven TLR: each peak marks one of the computational basis and its relative height corresponds to the probability superposed. With these joint spectral measurements, the generated Bell states of the two SCQs can be robustly confirmed without the standard tomographic technique. Furthermore, the statistical nonlocal-correlations between these two distant qubits can be directly read out by the joint spectral measurements, and consequently the Bell's inequality can be tested by sequentially measuring the relevant correlations related to the suitably-selected sets of the classical local variables $\{\theta_j,\theta_j', j=1,2\}$. The experimental challenges of our proposal are also analyzed.