Europhysics Letters

Are violations to temporal Bell inequalities there when somebody looks? (received ; accepted) PACS. 03.65Bz – Foundations, theory of measurement, miscellaneous theories (including Aha-ronov–Bohm effect, Bell inequalities, Berry's phase). PACS. 42.50Lc – Quantum fluctuations, quantum noise, and quantum jumps. PACS. 85.25Dq – Superconducting quantum interference devices (SQUIDs). Abstract. – The possibility of observing violations of temporal Bell inequalities, originally proposed by Leggett and Garg as a mean of testing the quantum mechanical delocalization of suitably chosen macroscopic bodies, is discussed by taking into account the effect of the measurement process. A general criterion quantifying this possibility is defined and shown not to be fulfilled by the various experimental configurations proposed so far to test inequalities of different forms. Introduction. – The validity of quantum mechanics at the macroscopic level is still an open question. Leggett and Garg [1] have challenged this question by proposing laboratory tests aimed at comparing, in a macroscopic domain, the predictions of a set of theories incorporating realism and non-invasivity, two properties not shared by quantum mechanics, versus quantum mechanics itself. The test involved certain inequalities, called temporal Bell inequalities in analogy to the well-known spatial ones [2]. These last have been already experimentally studied [3] to understand the validity of quantum mechanics against local realism at the microscopic level. Temporal Bell inequalities instead, involving correlation probabilities between subsequent measurements of the same observable, hold in realistic theories but are violated under certain conditions by quantum mechanics. The general ingredients required to discuss temporal Bell inequalities, regardless of the concrete scheme used, are three: (a) the possibility to have a coherent, quantum evolution of the state; (b) a dichotomic observable, already discrete or