Input-output theory for superconducting and photonic circuits that contain weak retro-reflections and other weak pseudo-cavities

TL;DR

This paper extends input-output theory to handle weak retro-reflections in superconducting and photonic circuits, enabling analysis of complex looped configurations and demonstrating near-perfect entanglement transmission despite imperfections.

Contribution

It introduces a novel method based on network-contraction theory to analyze circuits with weak loops, broadening the applicability of input-output theory in quantum circuit design.

Findings

Near-perfect entanglement transmission is achievable despite retro-reflections.

The new method effectively analyzes circuits with weak pseudo-cavities.

Optimal receiver design improves quantum communication fidelity.

Abstract

Input-output theory is invaluable for treating superconducting and photonic circuits connected by transmission lines or waveguides. However, this theory cannot in general handle situations in which retro-reflections from circuit components or configurations of beam-splitters create loops for the traveling-wave fields that connect the systems. Here, building upon the network-contraction theory of Gough and James [Commun. Math. Phys. 287, 1109 (2009)], we provide a compact and powerful method to treat any circuit that contains such loops so long as the effective cavities formed by the loops are sufficiently weak. Essentially all present-day on-chip superconducting and photonic circuits will satisfy this weakness condition so long as the reflectors that form the loops are not especially highly reflecting. As an example we analyze the problem of transmitting entanglement between two qubits connected by a transmission line with imperfect circulators, a problem for which the new method is essential. We obtain a full solution for the optimal receiver given that the sender employs a simple turn on/turn off. This solution shows that near-perfect transmission is possible even with significant retro-reflections.