Coherence, path predictability, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>I</mml:mi></mml:math> concurrence: A triality
Abhinash Kumar Roy, Neha Pathania, Nitish Kumar Chandra, Prasanta K. Panigrahi, Tabish Qureshi
Abstract
It is well known that fringe contrast is not a good quantifier of the wave nature of a quanton in multipath interference. An alternative interference visibility, based on the Hilbert-Schmidt coherence is introduced. It is demonstrated that this visibility is a good quantifier of wave nature and can be experimentally measured. A generalized path predictability is introduced, which reduces to the predictability of Greenberger and Yasin for the case of two paths. In a multipath, which-way interference experiment, the new visibility, the predictability, and the $I$ concurrence (quantifying the entanglement between the quanton and the path detector) are shown to follow a tight triality relation. It quantifies the essential role that entanglement plays in multipath quantum complementarity.