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Enhancing Protocol Privacy with Blind Calibration of Quantum Devices

Ankit Khandelwal, Stephen DiAdamo

TL;DR

This work tackles the privacy risk inherent in calibrating quantum channels by introducing blind calibration, where calibration states and the cost function are hidden from the receiver. The method randomizes the transmission order of a calibration set $S$ under a uniform distribution and performs the cost update at the sender side, preventing quantum state tomography from revealing protocol choices while still allowing efficient calibration. The authors formalize the protocol, outline assumptions, and validate its practicality through numerical simulations across random single-qubit states, BB84, entanglement swapping, and multipartite entanglement distribution under realistic noise models, demonstrating convergence within a few hundred iterations and robust performance under varied channel conditions. The proposed approach enhances protocol privacy in quantum networks and is general enough to apply to diverse quantum communication tasks, with potential extensions to more sophisticated decoding strategies and broader protocol suites.

Abstract

To mitigate the noise in quantum channels, calibration is used to tune the devices to minimize error. Generally, calibration is performed by transmitting pre-agreed-upon calibration states and determining an error cost so the two parties can tune their devices accordingly. The calibration states can be the same ones used for the desired protocol, and so an untrusted party could potentially learn which protocol is being performed by gathering knowledge of the calibration states and cost function. Here, we assume privacy of the protocol is the goal and therefore the receiver should not be allowed to determine the protocol states. We limit the information that is revealed to the receiver, and in this regard, we propose a simple protocol that hides the calibration states and cost function from the receiver, but still allows for calibration to be performed efficiently, thereby increasing the privacy of the protocol. We show various numerical results demonstrating the ability of the protocol under various channel noise parameters and communication scenarios.

Enhancing Protocol Privacy with Blind Calibration of Quantum Devices

TL;DR

This work tackles the privacy risk inherent in calibrating quantum channels by introducing blind calibration, where calibration states and the cost function are hidden from the receiver. The method randomizes the transmission order of a calibration set under a uniform distribution and performs the cost update at the sender side, preventing quantum state tomography from revealing protocol choices while still allowing efficient calibration. The authors formalize the protocol, outline assumptions, and validate its practicality through numerical simulations across random single-qubit states, BB84, entanglement swapping, and multipartite entanglement distribution under realistic noise models, demonstrating convergence within a few hundred iterations and robust performance under varied channel conditions. The proposed approach enhances protocol privacy in quantum networks and is general enough to apply to diverse quantum communication tasks, with potential extensions to more sophisticated decoding strategies and broader protocol suites.

Abstract

To mitigate the noise in quantum channels, calibration is used to tune the devices to minimize error. Generally, calibration is performed by transmitting pre-agreed-upon calibration states and determining an error cost so the two parties can tune their devices accordingly. The calibration states can be the same ones used for the desired protocol, and so an untrusted party could potentially learn which protocol is being performed by gathering knowledge of the calibration states and cost function. Here, we assume privacy of the protocol is the goal and therefore the receiver should not be allowed to determine the protocol states. We limit the information that is revealed to the receiver, and in this regard, we propose a simple protocol that hides the calibration states and cost function from the receiver, but still allows for calibration to be performed efficiently, thereby increasing the privacy of the protocol. We show various numerical results demonstrating the ability of the protocol under various channel noise parameters and communication scenarios.
Paper Structure (9 sections, 1 theorem, 2 equations, 7 figures, 1 algorithm)

This paper contains 9 sections, 1 theorem, 2 equations, 7 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Blind Calibration over Quantum Channels
  3. System Model and Simulation Configuration
  4. Protocol Performance Benchmarks
  5. Random Single-Qubit States
  6. BB84 States
  7. Entanglement-Swapping
  8. Multipartite Entanglement Distribution
  9. Conclusion

Key Result

Theorem 1

Given a state set $S_p = \{\rho_1, ..., \rho_i\} \subseteq \mathcal{S}(\mathcal{H})$, where $\dim(\mathcal{H}) = n$, and an $\epsilon>0$, there exists calibration set $S \supseteq S_p$, and $N$, the number of transmissions, such that, using Protocol proto:blind-calibration, a receiver following the

Figures (7)

  • Figure 1: The average infidelity vs. number of protocol iterations for calibration using $n=5$ randomly selected states over 50 km fiber under deterministic rotational noise.
  • Figure 2: Calibration result for mitigating (a) rotational noise, and (b) rotation, bit- and phase-flip noise optimized with $\epsilon_\text{th} = 10^{-7}$. Plotted is the average Quantum Bit Error Rate (QBER) for 350 trials of performing the BB84 protocol with 1,000 qubits sent per trial.
  • Figure 3: The calibration accuracy using a fixed $I_{\max}=20$ iterations over a noisy channel with both bit- and phase-flip and rotational error.
  • Figure 4: Entanglement swap circuit. The $BS$ gate prepares one of four Bell states. $N(p)$ gates apply noise.
  • Figure 5: Calibration performance for entanglement swapping under (a) rotational noise and (b) rotational and bit-flip noise optimized with a cost-change tolerance of $\epsilon_\text{th} = 10^{-7}$. Plotted is the average error rate for transmitting performing Bell state transmissions.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof