Optimal implementation of two-qubit linear optical quantum filters

TL;DR

This paper presents the design of optimal interferometric schemes for implementing two-qubit linear optical quantum filters, maximizing success probability through interference and conditioning in multiport interferometers.

Contribution

It introduces a method to design optimal linear optical quantum filters, including symmetric, asymmetric, and complex cases, enhancing success probabilities in quantum information processing.

Findings

Optimal interferometric schemes for two-qubit filters are developed.

Success probability is maximized for various filter types.

The approach extends to complex and asymmetric filters.

Abstract

We design optimal interferometric schemes for implementation of two-qubit linear optical quantum filters diagonal in the computational basis. The filtering is realized by interference of the two photons encoding the qubits in a multiport linear optical interferometer, followed by conditioning on presence of a single photon in each output port of the filter. The filter thus operates in the coincidence basis, similarly to many linear optical unitary quantum gates. Implementation of the filter with linear optics may require an additional overhead in terms of reduced overall success probability of the filtering and the optimal filters are those that maximize the overall success probability. We discuss in detail the case of symmetric real filters and extend our analysis also to asymmetric and complex filters.