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Deterministic entanglement distillation for secure double-server blind quantum computation
Lan Zhou, Yu-Bo Sheng
TL;DR
Double-server BQC removes the client’s need for quantum technology, but noisy channels can degrade the shared entanglement required by the protocol. This paper proposes an optical, hyperentanglement-based deterministic distillation protocol using QND measurement, obtaining a pure Bell state with 100% success in principle while preventing communication between the servers and feedback from the client.
Problem
Noisy channels can turn the shared entanglement into mixed states and make double-server BQC fail, while standard purification requires communication that may compromise its security.
Method
The paper uses hyperentanglement and optical quantum nondemolition measurement based on cross-Kerr nonlinearity to distill the shared entanglement.
Results
The protocol obtains the exact pure Bell state with success probability of 100% in principle from the Bobs’ measurement results.
Takeaways & Limitations
The distilled Bell states can be retained for subsequent BQC without classical communication between the Bobs or feedback from Alice.
Takeaways & Limitations
The Bobs may send wrong measurement results, causing Alice to identify the Bell state incorrectly and inducing computation errors.
Abstract
from arXiv · showhide
Blind quantum computation (BQC) provides an efficient method for the client who does not have enough sophisticated technology and knowledge to perform universal quantum computation. The single-server BQC protocol requires the client to have some minimum quantum ability, while the double-server BQC protocol makes the client's device completely classical, resorting to the pure and clean Bell-state shared by two servers. In this paper, we provide a deterministic entanglement distillation protocol in a practical noisy environment for the double-server BQC protocol. This protocol can obtain the pure maximally entangled Bell state with the success probability of 100% in principle. The distilled maximally entangled states can be remaind to perform the BQC protocol subsequently. The parties who perform the distillation protocol do not need to exchange the classical information and they learn nothing from the client. It makes this protocol unconditionally secure and suitable for current BQC protocol.
I. INTRODUCTION
Double-server BQC can make the client completely classical by relying on entanglement shared between two noncommunicating servers, but noisy channels degrade that resource. The paper proposes deterministic optical entanglement distillation using hyperentanglement and QND measurement, without client feedback to the servers.
- Motivation: Double-server BQC lets a completely classical client perform quantum computation through classical communication with two servers that cannot communicate with each other.This removes the quantum-technology requirement present in the single-server setting.
- Problem: Noisy channels degrade the shared entanglement and can make the double-server protocol fail, motivating recovery of mixed states into maximally entangled states.Standard entanglement purification methods require local operations and classical communication, raising security concerns in this setting.
- Contribution: The paper presents a deterministic optical distillation protocol based on hyperentanglement and quantum nondemolition measurement.The distillation equipment uses cross-Kerr nonlinearity, with polarization and spatial modes providing the hyperentangled resource.
- Contribution: The protocol obtains the exact Bell state with success probability of 100% in principle, according to the Bobs’ measurement results.Alice determines the Bell state from the reported outcomes without feeding information back to the Bobs.
- Security: The distilled entangled states can support subsequent BQC while the Bobs do not exchange classical information with each other.This avoids the mediation problem that could let one server indirectly send messages to the other through Alice.
II. DETERMINISTIC ENTANGLEMENT DISTILLATION WITH HYPERENTANGLEMENT
The protocol uses hyperentangled photon pairs and QND measurements to identify and distill Bell states deterministically from noisy shared states. Alice infers the Bell state from both Bobs’ measurement results without sending feedback, then the purified state supports double-server BQC.
- Distillation equipment: The setup employs quantum nondemolition measurements with cross-Kerr nonlinearity, coherent probe states, wave plates, and polarization beam splitters.The QND interaction changes probe-state phases according to the photon polarization and spatial mode.
- Hyperentangled input: A trust center distributes hyperentangled photon pairs whose spatial entanglement is used to purify polarization entanglement degraded by a noisy channel.The polarization component is modeled as a mixture of four Bell states, while the spatial component remains entangled.
- Bell-state identification: The two Bobs measure coherent-state phases using X-quadrature measurements, yielding two distinguishable outcomes that allow Alice to identify the exact Bell state.For matching outcomes, the protocol identifies |Φ+⟩; analogous measurement rules handle the other Bell-state cases.
- Integration with BQC: The protocol is integrated with double-server BQC by distilling noisy shared states, sending Alice the measurement results, and then running the standard BQC steps.Alice sends randomized angles to Bob1, Bob1 reports measurement results, and Alice and Bob2 continue the single-server BQC procedure.
- Security and reuse: Alice sends no feedback during distillation, preventing the Bobs from exchanging mediated messages while preserving the purified photon pair for subsequent computation.The QND-based procedure avoids the post-selection destruction associated with some earlier purification approaches.
III. DISCUSSION AND CONCLUSION
The protocol addresses the incompatibility between conventional entanglement purification and double-server BQC by preserving purified photon pairs without requiring classical communication between the Bobs. Its practical realization requires stable hyperentanglement in spatial and polarization degrees of freedom.
- Security and protocol suitability: Conventional purification protocols are unsuitable for double-server BQC because Alice-mediated message exchange can allow one Bob to communicate indirectly with the other.The proposed QND protocol preserves the photon pair and avoids this mediated exchange.
- Practical realization: The practical implementation requires generating hyperentanglement and stabilizing the spatial entanglement during operation.SPDC sources can generate hyperentanglement in spatial and polarization degrees of freedom.