Duality relation between coherence and path information in the presence of quantum memory

TL;DR

This paper establishes a new duality relation between coherence and path information in multipath interferometers when a quantum memory is involved, linking the bound to entanglement.

Contribution

It introduces a duality relation that accounts for quantum memory and entanglement, extending the understanding of wave-particle duality in quantum systems.

Findings

Derived a duality relation involving coherence and path information with quantum memory

Connected the duality bound to the entanglement between particle and quantum memory

Provided a generalized inequality for multipath interferometers in quantum settings

Abstract

The wave-particle duality demonstrates a competition relation between wave and particle behavior for a particle going through an interferometer. This duality can be formulated as an inequality, which upper bounds the sum of interference visibility and path information. However, if the particle is entangled with a quantum memory, then the bound may decrease. Here, we find the duality relation between coherence and path information for a particle going through a multipath interferometer in the presence of a quantum memory, offering an upper bound on the duality relation which is directly connected with the amount of entanglement between the particle and the quantum memory.