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arXiv:1101.2550

Testing Bell inequalities with circuit QEDs by joint spectral measurements

Hao Yuan, L. F. Wei, Jianhua Huang, X. H. Wang, Vlatko Vedral

Published Jan 13, 2011• 0 citations
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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 $\{θ_j,θ_j', j=1,2\}$. The experimental challenges of our proposal are also analyzed.

DOI
10.48550/arxiv.1101.2550

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We propose an approach to nondestructively detect NNN qubits by measuring the transmissions of a dispersively-coupled cavity. By taking into account all the cavity-qubits quantum correlations (i.e., beyond the usual coarse-grained/mean-field approximations), it is revealed that for an unknown normalized NNN-qubit state ∣ψN>=∑k=02N−1βk∣k>N|ψ_N>=\sum_{k=0}^{2^N-1}β_k|k>_N∣ψN​>=∑k=02N−1​βk​∣k>N​, each detected peak in the cavity transmitted spectra marks one of the basis states ∣k>N|k>_N∣k>N​ and the relative height of such a peak is related to the corresponding superposed-probability ∣βk∣2|β_k|^2∣βk​∣2. Our results are able to unambiguously account for the intriguing multi-peak structures of the spectra observed in a very recent circuit-quantum-electrodynamics experiment [Phys. Rev. A {\bf 81}, 062325 (2010)] with two superconducting qubits.
Using spectral joint measurements of the qubits, we propose a scheme to test the tripartite Mermin inequality with three qubits dispersively coupled to a driven cavity. First, we show how to generate a three-qubit Greenberger-Horne-Zeilinger (GHZ) state by only one-step quantum operation. Then spectral joint measurements are introduced to directly confirm such tripartite entanglement. Assisted by a series of single-qubit operations, these measurements are further utilized to test the Mermin inequality. The feasibility of the proposal is robustly demonstrated by the present numerical experiments.
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Bell inequality violation has been widely tested by using the bipartite entangled pure states and properly encoding the local observables in various experimental platforms, and the detector-, local-, and random loopholes have already been closed. A natural question is, how to deliver the Bell inequality violation by properly encoding the local observables? Here, we show that the Bell inequality violation is directly related to the coherence degree, which is controllable by encoding the different local observables into the entangled state. With the usual space-like correlation detections, we show that the coherence degree can be measured and thus the Bell nonlocality can be tested. The feasibility of the proposal is demonstrated by a numerical experiment typically with the cavity quantum electrodynamic system, in which the coherence degrees of the locally encoded bipartite entangled state can be conveniently measured by the spectral detection of the driven cavity. The present work might provide a feasible approach to verify the Gisin theorem, i.e., Bell inequality can be violated for any bipartite entangled pure state, once the local observables are properly encoded into the entangled state for keeping the desirable coherence.
An experimental scheme is proposed to test Bell's inequality by using superconducting nanocircuits. In this scheme, quantum entanglement of a pair of charge qubits separated by a sufficiently long distance may be created by cavity quantum electrodynamic techniques; the population of qubits is experimentally measurable by dc currents through the probe junctions, and one measured outcome may be recorded for every experiment. Therefore, both locality and detection-efficiency loopholes should be closed in the same experiment. We also propose a useful method to measure the amount of entanglement based on the concurrence between Josephson qubits. The measurable variables for Bell's inequality as well as the entanglement are expressed in terms of a useful phase-space Q function.