Ambiguous measurements, signaling, and violations of Leggett-Garg inequalities

Clive Emary

Ambiguous measurements do not reveal complete information about the system under test. Their quantum-mechanical counterparts are semiweak (or in the limit, weak) measurements and here we discuss their role in tests of the Leggett-Garg inequalities. We show that, while ambiguous measurements allow one to forgo the usual noninvasive measurability assumption, to derive a Leggett-Garg inequality that may be violated, we are forced to introduce another assumption that equates the invasive influence of ambiguous and unambiguous detectors. Based on this assumption, we derive signaling conditions that should be fulfilled for the plausibility of the Leggett-Garg test. We then propose an experiment on a three-level system with a direct quantum-optics realization that satisfies all signaling constraints and violates a Leggett-Garg inequality.

Swati Kumari, A. K. Pan

Kunkun Wang, Clive Emary, Mengyan Xu +4 more

We realize a quantum three-level system with photons distributed among three different spatial and polarization modes. Ambiguous measurements of the state of the qutrit are realized by blocking one out for the three modes at any one time. Using these measurements we construct a test of a Leggett-Garg inequality as well as tests of no-signaling-in-time for the measurements. We observe violations of the Leggett-Garg inequality that cannot be accounted for in terms of signaling. Moreover, we tailor the qutrit dynamics such that both ambiguous and unambiguous measurements are simultaneously nonsignaling, which is an essential step for the justification of the use of ambiguous measurements in Leggett-Garg tests.

Eduard Bordas Marchante

M. E. Goggin, M. V. de S. Almeida, Marco Barbieri +4 more

Kunkun Wang, Clive Emary, Mengyan Xu +4 more

© 2018 American Physical Society. We realize a quantum three-level system with photons distributed among three different spatial and polarization modes. Ambiguous measurements of the state of the qutrit are realized by blocking one out for the three modes at any one time. Using these measurements we construct a test of a Leggett-Garg inequality as well as tests of no-signaling-in-time for the measurements. We observe violations of the Leggett-Garg inequality that cannot be accounted for in terms of signaling. Moreover, we tailor the qutrit dynamics such that both ambiguous and unambiguous measurements are simultaneously nonsignaling, which is an essential step for the justification of the use of ambiguous measurements in Leggett-Garg tests.