Possibilities of a test of the temporal Bell inequalities using a flux qubit coupling to a dcSQUID

Although then last few years have seen tests of the temporal Bell inequalities (TBI) on microscopic systems with the use of ``ideal negative result'' (INR) measurements [1], and on macroscopic systems using weak measurement [2], to date there have been no tests on macroscopic systems using INR measurements. Moreover, in neither case was the assumption of noninvasiveness explicitly tested in an ancillary experiment [3,4]. Here we propose a complete INR protocol, including the ancillary experiment, for a test of the TBI on a macroscopic system, namely a flux qubit,with the measuring apparatus a dc SQUID. The general setup mirrors that of Knee et al. [1], with the nuclear spins replaced by the flux qubit and the electron spins by the dc SQUID, and we analyze the relation between the theoretical concept of ``venality''" introduced in ref. [1] and the experimental behavior expected in our ancillary test. On the basis of this analysis we assess the current feasibility of the proposed experiment.\\[4pt] [1] G. C.Knee et al., Nature Comm. 3, 606 (2012).\\[0pt] [2] A. Palacios-Laloy et al., Nature Phys. 6, 442(2010).\\[0pt] [3] A. J. Leggett, Found. Phys.18, 939 (1988).\\[0pt] [4] A.Mizel and A.Wilde, Found. Phys. 42, 256-265(2012).