Quantum which-way information and fringe visibility when the detector is entangled with an ancilla
J. Prabhu Tej, A. R. Usha Devi, H. S. Karthik, Sudha, A. K. Rajagopal · Physical Review A · 2014
Quantum-mechanical wave-particle duality is quantified in terms of a trade-off relation between the fringe visibility and the which-way distinguishability in an interference experiment. This relation was recently generalized by Banaszek et al. [Nat. Commun. 4, 2594 (2013)] when the particle is equipped with an internal degree of freedom such as spin. Here, we extend the visibility-distinguishability trade-off relation to quantum interference of a particle possessing an internal degree of freedom, when the which-way detector state is entangled with an ancillary system. We introduce an extended which-way distinguishability ${\mathcal{D}}_{E}$ and the associated extended fringe visibility ${\mathcal{V}}_{E}$, satisfying the inequality ${\mathcal{D}}_{E}^{2}+{\mathcal{V}}_{E}^{2}\ensuremath{\le}1$ in this scenario. We illustrate, with the help of three specific examples, that while the which-way information inferred solely from the detector state (without ancilla) vanishes, the extended distinguishability retrievable via measurements on the detector-ancilla entangled state is nonzero. Furthermore, in all the three examples, the extended visibility and the generalized visibility (which was introduced by Banaszek et al.) match identically with each other.