Semi-device-independent certification of high-dimensional quantum channels

TL;DR

This paper introduces a semi-device-independent method to certify high-dimensional quantum channels using observed data and structural constraints, enabling reliable assessment without fully trusted devices.

Contribution

It develops a novel certification framework leveraging the Choi-Jamio{}kowski isomorphism and introduces new witnesses for entanglement dimensionality and fidelity.

Findings

Successfully reproduces analytical benchmarks.

Validates the method on dephasing and depolarizing channels.

Provides lower bounds on entanglement fidelity from observed data.

Abstract

Certifying high-dimensional quantum channels is essential for ensuring the reliability of quantum communication protocols. Existing certification schemes often rely on fully trusted internal devices, which is difficult to achieve in realistic scenarios. Here, we propose a semi-device-independent framework for certifying channel properties directly from observed statistics, assuming only that the system dimension is known. By explicitly incorporating the full set of structural constraints inherent to Choi states, our approach exploits the Choi-Jamio{\l}kowski isomorphism for rigorous certification of quantum channels. The entanglement dimensionality of quantum channels is first certified by introducing a witness and numerically determining its Schmidt-number-dependent bounds. This certification method reproduces known analytical benchmarks and is applied to dephasing and depolarizing noise channels, thereby confirming its validity. To provide a more complete assessment of channel performance, the entanglement fidelity of quantum channels is also certified using a hierarchy of semidefinite programming relaxations based on localizing matrices. Lower bounds on the entanglement fidelity are obtained that are compatible with either the full set of observed statistics or a single witness value.