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arXiv:quant-ph/0304156 · Physical Review A

Testing Bell’s inequality and measuring the entanglement using superconducting nanocircuits

Guang-Ping He, Shi-Liang Zhu, Z. D. Wang, Huazhong Li

Published Jul 15, 2003• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.68.012315

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Journal of Modern Physics•Jan 1, 2011•0 citations
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.
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). By using the recently demonstrated entanglement between single trapped atoms and single photons it becomes possible to entangle two atoms at a large distance via entanglement swapping. Combining the high detection efficiency achieved with atoms with the space-like separation of the atomic state detection events, both loopholes can be closed within the same experiment. In this paper we present estimations based on current experimental achievements which show that such an experiment is feasible in future.
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). By using the recently demonstrated entanglement between single trapped atoms and single photons it becomes possible to entangle two atoms at a large distance via entanglement swapping. Combining the high detection efficiency achieved with atoms with the space-like separation of the atomic state detection events, both loopholes can be closed within the same experiment. In this paper we present estimations based on current experimental achievements which show that such an experiment is feasible in future.
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}\{|kl>,\,k,l=0,1\}{∣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 {θj,θj′,j=1,2}\{θ_j,θ_j', j=1,2\}{θj​,θj′​,j=1,2}. The experimental challenges of our proposal are also analyzed.
Abstract Superposition, entanglement and non-locality constitute fundamental features of quantum physics. The fact that quantum physics does not follow the principle of local causality1–3 can be experimentally demonstrated in Bell tests4 performed on pairs of spatially separated, entangled quantum systems. Although Bell tests, which are widely regarded as a litmus test of quantum physics, have been explored using a broad range of quantum systems over the past 50 years, only relatively recently have experiments free of so-called loopholes5 succeeded. Such experiments have been performed with spins in nitrogen–vacancy centres6, optical photons7–9 and neutral atoms10. Here we demonstrate a loophole-free violation of Bell’s inequality with superconducting circuits, which are a prime contender for realizing quantum computing technology11. To evaluate a Clauser–Horne–Shimony–Holt-type Bell inequality4, we deterministically entangle a pair of qubits12 and perform fast and high-fidelity measurements13 along randomly chosen bases on the qubits connected through a cryogenic link14 spanning a distance of 30 metres. Evaluating more than 1 million experimental trials, we find an average S value of 2.0747 ± 0.0033, violating Bell’s inequality with a P value smaller than 10−108. Our work demonstrates that non-locality is a viable new resource in quantum information technology realized with superconducting circuits with potential applications in quantum communication, quantum computing and fundamental physics15.
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.
So far, all experimental tests of Bell inequalities which must be satisfied by all local realistic hidden-variable theories and are violated by quantum mechanical predictions have left at least one loophole open. We propose a feasible setup allowing for a loophole-free test of the Bell inequalities. Two electron spin qubits of donors31P in a nanoscale silicon host in different cavities 300 m apart are entangled through a bright coherent light and postselections using homodyne measurements. The electron spins are then read out randomly and independently by Alice and Bob, respectively, with unity efficiency in less than 0.7 µs by using optically induced spin to charge transduction detected by radio-frequency single electron transistor. A violation of Bell inequality larger than 37% and 18% is achievable provided that the detection accuracy is 0.99 and 0.95, respectively.