Effect of frequency mismatched photons in quantum information processing

TL;DR

This paper investigates how frequency mismatches in photons affect quantum information processing schemes, emphasizing the importance of detector time resolution in maintaining high fidelity and interference visibility.

Contribution

It provides a detailed analysis of frequency mismatch effects on QIP protocols and highlights the critical role of detector response time in mitigating these issues.

Findings

Fidelity depends on detector time resolution in distributed QIP.

Reduced interference visibility occurs with slower detectors.

Fast detectors can overcome frequency mismatch problems.

Abstract

Many promising schemes for quantum information processing (QIP) rely on few-photon interference effects. In these proposals, the photons are treated as being indistinguishable particles. However, single photon sources are typically subject to variation from device to device. Thus the photons emitted from different sources will not be perfectly identical, and there will be some variation in their frequencies. Here, we analyse the effect of this frequency mismatch on QIP schemes. As examples, we consider the distributed QIP protocol proposed by Barrett and Kok, and Hong-Ou-Mandel interference which lies at the heart of many linear optical schemes for quantum computing. In the distributed QIP protocol, we find that the fidelity of entangled qubit states depends crucially on the time resolution of single photon detectors. In particular, there is no reduction in the fidelity when an ideal detector model is assumed, while reduced fidelities may be encountered when using realistic detectors with a finite response time. We obtain similar results in the case of Hong-Ou-Mandel interference -- with perfect detectors, a modified version of quantum interference is seen, and the visibility of the interference pattern is reduced as the detector time resolution is reduced. Our findings indicate that problems due to frequency mismatch can be overcome, provided sufficiently fast detectors are available.