Investigating the optimality of ancilla-assisted linear optical Bell measurements

TL;DR

This paper investigates the optimality of ancilla-assisted linear optical Bell measurements, providing analytical bounds and numerical methods to evaluate and improve measurement success probabilities with various ancillary states.

Contribution

It introduces an analytical upper bound for success probability and a numerical optimization approach, exploring new ancilla states beyond previous studies.

Findings

Analytical upper bound matches existing schemes' success probabilities.

Numerical methods confirm optimality of small known schemes.

Exploration of new ancillary states with potential for improved performance.

Abstract

In the last decade Grice and Ewert and van Loock found linear optical networks achieving near-unit efficiency unambiguous Bell state discrimination, when fed with increasingly complex ancillary states. However, except for the vacuum ancilla case, the optimality of these schemes is unknown. Here, the optimality of these networks is investigated through analytical and numerical means. We show an analytical upper bound to the success probability for interferometers that preserve the polarization of the input photons, saturated by both Grice's and Evert-van Loock's strategies. Furthermore, such an upper bound links the complexity of their ancilla states with the scaling of their performance. We also show a computer-aided approach to the optimization of such measurement schemes for generic interferometers, by simulating an optical network supplied with various kinds of ancillary input states. We numerically confirms the optimality of known small schemes. We use both methods to investigate other ancilla states, some of them never studied before.