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Composably Secure Delegated Quantum Computation with Weak Coherent Pulses

Maxime Garnier, Dominik Leichtle, Luka Music, Harold Ollivier

TL;DR

This paper tackles reducing the client’s quantum resources in Secure Delegated Quantum Computation by using Weak Coherent Pulses (WCPs) to realize composably secure SDQC. It introduces a BatchRSP primitive that guarantees at least one single-photon state in a batch, which is then processed via privacy amplification to yield a secure single qubit for SDQC, and shows composable security in the Abstract Cryptography framework. A two-intensity instantiation achieves improved low-transmittance scaling of $1/\eta^2$ (versus the prior $1/\eta^4$ in earlier WCP-based schemes) and reveals robustness to WCP imperfections and practical streaming integration, enabling longer distances between client and server. The work also clarifies weaknesses in standard decoy-state QKD proofs, and demonstrates how the same batch-state approach strengthens QKD security arguments while remaining resource-efficient.

Abstract

A client can delegate a quantum computation to a powerful remote server while ensuring the privacy and the integrity of its computation via Secure Delegated Quantum Computation (SDQC). Thanks to recent results making them noise-robust and resource-efficient, proofs-of-concept implementations of generic SDQC protocols have already been demonstrated. Yet, the requirements for implementing them are still too stringent to go beyond this step while maintaining high security expectations. To further reduce their physical resource cost, we show how to realise SDQC using weak coherent pulses (WCPs) instead of single photons. More precisely, we construct a protocol which guarantees that, among a sufficiently large batch of transmitted WCPs, at least one contained only a single photon. This holds even if the adversary controls the transmittance of the photonic link connecting the client and the server. Our protocol's security is proven in the composable Abstract Cryptography (AC) framework. This batch can then be fed to known quantum privacy amplification techniques to prepare a single secure qubit in the X-Y plane, which can be used in any composable SDQC protocol which relies on the secure preparation of single qubits. Furthermore, the guarantee on the batch of states can also be used for Quantum Key Distribution (QKD) where the privacy amplification step is classical. In doing so, we address a weakness in the standard security proof of the decoy state method. While our protocol can be instantiated with any number of different intensities for the WCPs, using only two intensities already shows improved scaling at low transmittance, thus opening the possibility of increasing the distance between the client and the server.

Composably Secure Delegated Quantum Computation with Weak Coherent Pulses

TL;DR

This paper tackles reducing the client’s quantum resources in Secure Delegated Quantum Computation by using Weak Coherent Pulses (WCPs) to realize composably secure SDQC. It introduces a BatchRSP primitive that guarantees at least one single-photon state in a batch, which is then processed via privacy amplification to yield a secure single qubit for SDQC, and shows composable security in the Abstract Cryptography framework. A two-intensity instantiation achieves improved low-transmittance scaling of (versus the prior in earlier WCP-based schemes) and reveals robustness to WCP imperfections and practical streaming integration, enabling longer distances between client and server. The work also clarifies weaknesses in standard decoy-state QKD proofs, and demonstrates how the same batch-state approach strengthens QKD security arguments while remaining resource-efficient.

Abstract

A client can delegate a quantum computation to a powerful remote server while ensuring the privacy and the integrity of its computation via Secure Delegated Quantum Computation (SDQC). Thanks to recent results making them noise-robust and resource-efficient, proofs-of-concept implementations of generic SDQC protocols have already been demonstrated. Yet, the requirements for implementing them are still too stringent to go beyond this step while maintaining high security expectations. To further reduce their physical resource cost, we show how to realise SDQC using weak coherent pulses (WCPs) instead of single photons. More precisely, we construct a protocol which guarantees that, among a sufficiently large batch of transmitted WCPs, at least one contained only a single photon. This holds even if the adversary controls the transmittance of the photonic link connecting the client and the server. Our protocol's security is proven in the composable Abstract Cryptography (AC) framework. This batch can then be fed to known quantum privacy amplification techniques to prepare a single secure qubit in the X-Y plane, which can be used in any composable SDQC protocol which relies on the secure preparation of single qubits. Furthermore, the guarantee on the batch of states can also be used for Quantum Key Distribution (QKD) where the privacy amplification step is classical. In doing so, we address a weakness in the standard security proof of the decoy state method. While our protocol can be instantiated with any number of different intensities for the WCPs, using only two intensities already shows improved scaling at low transmittance, thus opening the possibility of increasing the distance between the client and the server.

Paper Structure

This paper contains 25 sections, 10 theorems, 39 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Contributions and Related Work
  3. Preliminaries
  4. Modelling Weak Coherent Pulses
  5. Batch State Preparation from Weak Coherent Pulses with Composable Security
  6. An Instantiation with Two Intensities
  7. Maximal reachable intensity.
  8. Discussion
  9. Intuition for the accept criterion of Algorithm $\mathcal{B}$
  10. Improved Security
  11. Improved practicality
  12. Improved security for QKD
  13. Acknowledgements
  14. Proof of Theorem \ref{['thm:decoy-realization']}
  15. Bounding simulation failure by Game \ref{['game:security']}.
  16. ...and 10 more sections

Key Result

Theorem 1

The protocol from KKLM23asymmetric uses $\mathsf{BatchRSP}$ as a primitive to perform SDQC for $\mathsf{BQP}$ with information-theoretic composable security and negligible security error.

Figures (13)

  • Figure 1: $\mathsf{WCPGenerator}$
  • Figure 2: $\mathsf{BatchRSP}$
  • Figure 3: Multi-Intensity Weak Coherent Pulse Method
  • Figure 4: Correctness of the Multi-Intensity Weak Coherent Pulse Method
  • Figure 5: Security of the Multi-Intensity Weak Coherent Pulse Method
  • ...and 8 more figures

Theorems & Definitions (20)

  • Theorem 1: SDQC from Batch Remote State Preparation KKLM23asymmetric, informal
  • Remark 1
  • Theorem 2
  • Corollary 1
  • Theorem 3: Correctness and Security Errors
  • proof : Correctness error --- Proof sketch
  • proof : Security error --- Proof sketch
  • Theorem 4: Scaling for $\eta \rightarrow 0$
  • proof : Scaling --- Proof Sketch
  • Theorem 5
  • ...and 10 more