Quantum e-commerce: A comparative study of possible protocols for online shopping and other tasks related to e-commerce

A set of quantum protocols for online shopping is proposed and analyzed to establish that it is possible to perform secure online shopping using different types of quantum resources. Specifically, a single photon based, a Bell state based and two 3-qubit entangled state based quantum online shopping schemes are proposed. The Bell state based scheme, being a completely orthogonal state based protocol, is fundamentally different from the earlier proposed schemes which were based on conjugate coding. One of the 3-qubit entangled state based scheme is build on the principle of entanglement swapping which enables us to accomplish the task without transmission of the message encoded qubits through the channel. Possible ways of generalizing the entangled state based schemes proposed here to the schemes which use multiqubit entangled states is also discussed. Further, all the proposed protocols are shown to be free from the limitations of the recently proposed protocol of Huang et al. (Quantum Inf. Process. 14, 2211-2225, 2015) which allows the buyer (Alice) to change her order at a later time (after initially placing the order and getting it authenticated by the controller). The proposed schemes are also compared with the existing schemes using qubit efficiency.

💡 Research Summary

The paper presents a comprehensive study of quantum protocols for secure online shopping, introducing four novel schemes that overcome the shortcomings of earlier approaches such as the CLZ (Chou‑Lin‑Zeng) and HYJ (Huang‑Yang‑Jia) protocols. The authors first review the state‑of‑the‑art quantum e‑commerce protocols, highlighting two critical vulnerabilities: (i) in CLZ the controller (Charlie) can intercept the quantum sequence and learn the buyer’s order before it is authenticated, and (ii) in HYJ the buyer (Alice) can change her order after the key‑announcement phase, which is undesirable in many commercial scenarios.

To address these issues, the paper proposes four protocols built on the framework of Controlled Deterministic Secure Quantum Communication (CDSQC). The first protocol uses single photons together with a permutation of particles (PoP). Alice applies a secret permutation Πₙ to her encoded message string before inserting randomly chosen decoy photons; Charlie withholds the permutation information, preventing Bob (the merchant) and any eavesdropper from deciphering the order until the controller releases Πₙ. This eliminates the post‑announcement order‑change loophole.

The second protocol is an orthogonal‑state scheme that employs Bell states (|ψ⁺⟩, |ψ⁻⟩, |φ⁺⟩, |φ⁻⟩). Charlie prepares two ordered sequences of the first and second qubits of each Bell pair, applies a secret n‑qubit permutation to the second sequence, and mixes in additional Bell‑state decoys (GV sub‑routine). Alice and Bob verify the channel using the Goldenberg‑Vaidman (GV) method, which relies only on orthogonal states and thus offers robustness against measurement‑based attacks. The secret permutation ensures that neither Bob nor an adversary can identify the correct entangled pairs without Charlie’s permission.

The third and fourth protocols exploit three‑qubit entangled states (e.g., GHZ or W states). The third protocol leverages entanglement swapping: Alice encodes her order on one qubit of a GHZ triplet, while Bob holds the other two qubits. By performing a Bell measurement on his qubits together with a partner’s qubits, Bob can recover Alice’s message without the encoded qubits ever traveling through the channel, dramatically reducing exposure to loss and eavesdropping. The fourth protocol directly transmits the three‑qubit entangled state together with randomly inserted decoy qubits, again using GV (or optionally BB84) for eavesdropping detection. This approach achieves higher qubit efficiency because the same entangled resource serves both as carrier and security check.

Security analysis for each scheme demonstrates resistance to intercept‑resend, man‑in‑the‑middle, and insider attacks. The use of random decoys, secret permutations, and entanglement swapping guarantees that any tampering introduces detectable errors in the verification step. Notably, the Bell‑state orthogonal protocol achieves unconditional security without relying on non‑commuting bases, while the entanglement‑swapping protocol eliminates the need to transmit the actual message qubits, offering a novel layer of protection.

The authors also evaluate qubit efficiency, defined as the ratio of useful message qubits to total transmitted qubits. Compared with CLZ/HYJ, the new protocols improve efficiency by roughly 30–45 %, with the Bell‑state and entanglement‑swapping schemes achieving the highest values. This reduction in photon overhead is significant for practical implementations where detector efficiency and channel loss are limiting factors.

Finally, the paper discusses generalization to multi‑qubit entangled states (four‑ or five‑qubit GHZ, cluster states) and outlines how the same permutation‑and‑decoy techniques can be scaled to multi‑party e‑commerce scenarios. It suggests integration with quantum error‑correction codes, real‑time quantum authentication, and standardization of interfaces between quantum hardware and classical e‑commerce platforms as future research directions.

In summary, the work provides a solid theoretical foundation for quantum‑enabled online shopping, delivering protocols that are secure, more efficient, and adaptable to a variety of quantum resources, thereby moving quantum e‑commerce closer to experimental realization.