LETTERS Violation of Bell’s inequality in Josephson phase qubits Markus Ansmann 1 , H. Wang 1 , Radoslaw C. Bialczak 1 , Max Hofheinz 1 , Erik Lucero 1 , M. Neeley 1 , A. D. O’Connell 1 , D. Sank 1 , M. Weides 1 , J. Wenner 1 , A. N. Cleland 1 & John M. Martinis 1 The measurement process plays an awkward role in quantum mechanics, because measurement forces a system to ‘choose’ between possible outcomes in a fundamentally unpredictable manner. Therefore, hidden classical processes have been consid- ered as possibly predetermining measurement outcomes while preserving their statistical distributions 1 . However, a quantitative measure that can distinguish classically determined correlations from stronger quantum correlations exists in the form of the Bell inequalities, measurements of which provide strong experimental evidence that quantum mechanics provides a complete descrip- tion 2–4 . Here we demonstrate the violation of a Bell inequality in a solid-state system. We use a pair of Josephson phase qubits 5–7 acting as spin-1/2 particles, and show that the qubits can be entangled 8,9 and measured so as to violate the Clauser–Horne– Shimony–Holt (CHSH) version of the Bell inequality 10 . We measure a Bell signal of 2.0732 6 0.0003, exceeding the maximum amplitude of 2 for a classical system by 244 standard deviations. In the experiment, we deterministically generate the entangled state, and measure both qubits in a single-shot manner, closing the detec- tion loophole 11 . Because the Bell inequality was designed to test for non-classical behaviour without assuming the applicability of quantum mechanics to the system in question, this experiment provides further strong evidence that a macroscopic electrical circuit is really a quantum system 7 . In classical physics, deterministic laws provide a complete descrip- tion for the evolution of a physical system. Quantum physics purports to provide an equally complete description, but the measurement process involves additional premises, and measurement outcomes are intrinsically uncertain. When performing measurements on entangled particles, however, the unpredictability of measurement is combined with very strong correlations between measurements on the individual particles, leading to the apparently paradoxical thought experiments developed by Einstein, Podolsky and Rosen 12 . The CHSH protocol 10 describes one such experiment, with a stati- stical test to distinguish classical pre-determination from quantum theory. This protocol uses a pair of spin-1/2 particles A and B, with spin states j0æ and j1æ, which are entangled in the Bell singlet 01 j i{ 10 j i ð Þ  ffiffi 2 p . The entangled spins are separated and measured independently along one of two directions (a and a9 for spin A, b and b9 for spin B). The measurements yield a 0 or 1 for each spin, regardless of the measurement axis. For x g a, a9 and y g b, b9, we define the correlation E(x, y) for the two spins as the difference in the probabil- ities of measuring the same result versus measuring a different result Ex , y ð Þ~P same x , y ð Þ{P diff x , y ð Þ ~P 00 x , y ð ÞzP 11 x , y ð Þ{P 01 x , y ð Þ{P 10 x , y ð Þ ð1Þ The Bell signal S is then defined as S~Ea, b ð ÞzEa’, b ð Þ{Ea, b’ ð ÞzEa’, b’ ð Þ ð2Þ Classical (predetermined) outcomes result in a Bell signal jSj # 2, whereas quantum mechanics permits a larger signal S jjƒ2 ffiffi 2 p ~2:828, for the appropriate measurement axes. Completely random outcomes result in S 5 0. An experiment returns a Bell violation if jSj . 2, and thus indicates quantum entanglement. The derivation of the limit jSj # 2 is based on two assumptions, which, if not met, provide loopholes that, in principle, allow an experiment to return a Bell violation even for a classically predeter- mined process. The first loophole is called the ‘detection loophole’ 11 and affects experiments in which the spin measurement is ineffective, for example not detecting one of the spins, or confusing a spin from one pair with that of another. This breaks the assumption that a measurement always returns a 0 or 1 for both particles in the pair, because it allows for the additional measurement outcome of ‘undetected’ or incorrect pair identification. This loophole com- monly affects experiments based on the measurement of entangled photons 4 , because a fraction of these are missed by even the best available photon detectors. The reported data set then consists of only a subset of the entire ensemble of entangled photons, a subset whose detection could introduce an unknown classical correlation. This loophole is commonly countered by the ‘fair-sampling hypo- thesis’, which claims that no such correlation should exist. The second loophole, the ‘locality/causality loophole’, applies when the spin measurements are not performed with true space-like separation, allowing the spins in principle to communicate during the measurement. This loophole affects experiments where the distance d between the spins during measurement does not fulfill d $ ct meas , where t meas specifies the time it takes to completely measure the spins and c is the speed of light. A variety of experiments have shown violations of the Bell in- equality 13–15 with one or the other of these loopholes closed. With the caveat that no one experiment has closed both loopholes, it appears that quantum mechanics provides a more accurate descrip- tion than do local hidden variable theories. Here we describe measurements on a pair of Josephson phase qubits, serving as spin-1/2 particles, which are entangled via an elec- tromagnetic resonator 16,17 . Given that we can generate the entangled pair with certainty and obtain a measurement of each qubit every time, our experiment is not subject to the detection loophole and does not need to invoke the fair-sampling hypothesis. However, the qubits are separated by only 3.1 mm, and with the measurement process lasting around 30 ns our experiment cannot close the locality loophole. The Josephson phase qubit, as described previously 18 , has qubit states j0æ and j1æ whose energy difference E 10 can be adjusted by an external current bias. By also applying microwaves at the transition 1 Department of Physics, University of California, Santa Barbara, California 93106, USA. Vol 461 | 24 September 2009 | doi:10.1038/nature08363 504 Macmillan Publishers Limited. All rights reserved ©2009