Quantum which-way information and fringe visibility when the detector is entangled with an ancilla

TL;DR

This paper extends the quantum wave-particle duality trade-off to scenarios where the which-way detector is entangled with an ancilla, revealing hidden which-way information and linking extended and generalized visibilities.

Contribution

It introduces an extended which-way distinguishability and fringe visibility for entangled detector-ancilla systems, generalizing previous duality relations in quantum interference.

Findings

Extended distinguishability is non-zero even when detector alone shows no which-way info.

Extended and generalized visibilities are shown to be equal in the examples.

The new framework reveals hidden which-way information via entanglement.

Abstract

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 is recently generalized by Banaszek et. al., (Nature Communications 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 and the associated extended fringe visibility satisfying the duality inequality 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 non-zero. Furthermore, in all the three examples, the extended visibility and the generalized visibility (which was introduced by Banaszek et. al., Nature Communications 4, 2594, 2013)) match identically with each other.