[Paper Review] Quantum Error Models and Error Mitigation for Long-Distance Teleportation Architectures

Jeffrey H. Shapiro, Joe Aung+1 more|ArXiv.org|Nov 14, 2002

Quantum Information and Cryptography3 citations

TL;DR

This paper proposes a long-distance quantum teleportation architecture using ultrabright narrowband entangled photons and trapped-atom quantum memories, enabling high-fidelity qubit transfer over standard fiber. It models single-photon loading events and demonstrates that quantum error correction and entanglement purification significantly improve fidelity, especially in Greenberger-Horne-Zeilinger (GHZ) state protocols for quantum secret sharing.

ABSTRACT

A quantum communication architecture is being developed for long-distance, high-fidelity qubit teleportation. It uses an ultrabright narrowband source of polarization-entangled photons, plus trapped-atom quantum memories, and it is compatible with long-distance transmission over standard telecommunication fiber. This paper reports error models for the preceding teleportation architecture, and for an extension thereto which enables long-distance transmission and storage of Greenberger-Horne-Zeilinger states. The use of quantum error correction or entanglement purification to improve the performance of these quantum communication architectures is also discussed.

Motivation & Objective

• To develop a quantum communication architecture for long-distance, high-fidelity qubit teleportation using entangled photons and trapped-atom memories.
• To model single-photon loading events in the MIT/NU quantum communication system to quantify error sources and fidelity degradation.
• To evaluate the performance of quantum error correction and entanglement purification in improving fidelity for teleportation and GHZ state distribution.
• To extend the architecture to support long-distance transmission and storage of GHZ states for quantum secret sharing (QSS) protocols.
• To compare the performance of dual-DPA and heralded-plus-DPA GHZ systems with and without error correction under realistic loss and decoherence conditions.

Proposed method

• Uses an ultrabright narrowband source of polarization-entangled photons generated via two coherently pumped type-II phase-matched optical parametric amplifiers on a polarizing beam splitter.
• Employs quantum-state frequency conversion to shift photon wavelengths from 1.55 µm (low-loss fiber window) to 795 nm (matching rubidium atom cavity linewidths) for memory loading.
• Applies time-division multiplexing and polarization restoration to enable long-distance transmission over standard telecommunication fiber.
• Models single-photon loading events using event-based fidelity metrics, incorporating photon loss, memory decay, and detector inefficiencies.
• Introduces a five-qubit error-correcting code and an entanglement purification protocol to correct errors in teleportation and GHZ state distribution.
• Derives analytical expressions for average fidelity in quantum secret sharing (QSS) protocols: $ F = P_{G} + 2P_{e1}/3 + 2P_{e2}/3 $ for dual-DPA and $ F = P_{G} + 2P_{e1}/3 + P_{e2} $ for heralded-plus-DPA.

Experimental results

Research questions

• RQ1 How does the fidelity of long-distance qubit teleportation degrade under realistic loss and decoherence in the MIT/NU architecture?
• RQ2 To what extent can quantum error correction improve fidelity in GHZ state distribution for quantum secret sharing?
• RQ3 How does entanglement purification enhance the performance of long-distance quantum communication systems with imperfect sources and memories?
• RQ4 What is the comparative performance of dual-DPA and heralded-plus-DPA GHZ systems under error correction and varying path lengths?
• RQ5 At what point does error correction become detrimental due to multi-qubit error rates in the dual-DPA system?

Key findings

• The heralded-plus-DPA GHZ system outperforms the dual-DPA system in average QSS fidelity under both coded and uncoded conditions.
• Quantum error correction improves fidelity for the heralded-plus-DPA system across all path lengths tested, with significant gains at longer distances.
• For the dual-DPA system, error correction reduces fidelity beyond approximately 16 km path length due to high incidence of multi-qubit errors.
• The fidelity of the QSS protocol is quantified by $ F = P_{G} + 2P_{e1}/3 + 2P_{e2}/3 $ for dual-DPA and $ F = P_{G} + 2P_{e1}/3 + P_{e2} $ for heralded-plus-DPA, with $ P_G $, $ P_{e1} $, and $ P_{e2} $ representing probabilities of successful, single-error, and double-error loading events.
• Entanglement purification and error correction are shown to be effective in mitigating the effects of photon loss, memory decay, and detector inefficiencies in long-distance quantum communication.