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Bulletin of the American Physical Society

Attempt to Violate the CHSH Bell Inequality in Josephson Phase Qubits

M. Ansmann, Radoslaw C. Bialczak, Nadav Y. Katz, E. Lucero, R. McDermott, M. Neeley, A. D. O’Connell, Matthias Steffen, Eva Maria Weig, A.N. Cleland, John M. Martinis

Published Mar 6, 2007• 0 citations
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In this paper we study the nonlocal properties of two-qubit Werner states parametrized by the visibility parameter $0\ensuremath{\leqslant}p\ensuremath{\leqslant}1$. A family of Bell inequalities is constructed that proves the two-qubit Werner states to be nonlocal for the parameter range $0.7056<p\ensuremath{\leqslant}1$. This is slightly wider than the range $0.7071<p\ensuremath{\leqslant}1$, corresponding to the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. This answers a question posed by Gisin in the positive, i.e., there exist Bell inequalities which are more efficient than the CHSH inequality in the sense that they are violated by a wider range of two-qubit Werner states.
We analyze conditions for violation of the Bell inequality in the Clauser-Horne-Shimony-Holt form, focusing on Josephson phase qubits. We start the analysis with maximum violation in the ideal case, and then take into account the effects of local measurement errors and decoherence. Special attention is paid to configurations of the qubit measurement directions in the pseudospin space lying within either horizontal or vertical planes; these configurations are optimal in certain cases. Besides local measurement errors and decoherence, we also discuss the effect of measurement crosstalk, which affects both the classical inequality and the quantum result. In particular, we propose a version of the BI which is insensitive to the crosstalk.