Single-quanta interferometry: which-way versus which-phase information stored in an ancillary quantum system

TL;DR

This paper compares which-way and which-phase information in a quantum interferometer using Shannon entropy, showing their relationship under certain conditions and proposing an experimental setup for verification.

Contribution

It introduces a theoretical comparison of which-way and which-phase information in quantum interferometry using entropy measures and proposes an experimental design for validation.

Findings

Which-phase information is less than or equal to which-way information in pure bipartite states.

Equality of information measures holds under symmetric conditions.

Measurement for one type of information does not reveal the other.

Abstract

In interferometers, the more information about the quanta's path available in an ancillary quantum system (AQS), the less visibility the interference has. By use of Shannon entropy, we try to compare the amount of which-phase information with the amount of which-way information stored in the AQS of two-path interferometers with symmetric beam merging. We show that the former is lower than or equal the latter if the bipartite system of the single-quanta and the AQS is initially prepared in a pure state and the interaction between the two parts is unitary. Especially when there exists symmetry, the equality holds. No which-way information is obtained by the measurement that we use for extracting the which-phase information and vice versa. In order to verify the results experimentally, we propose assembling a new single-photon interferometer.