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International Conference on Mobile, Military, Maritime IT Convergence (ICMIC)

Quantum Code-Assisted Entanglement Distillation Under Bit-Flip Noise

Huidan Zheng, Gunsik Min, Yujin Kang, Youshin Chung, Hyelyn Kwak, Jun Heo

Published Aug 27, 2025• 0 citations
Publisher

Abstract

This paper investigates entanglement distillation protocols assisted by quantum codes under bit-flip noise. Three protocols are compared: repetition code in correction and detection modes, and the [[4, 2, 2]] code in detection mode. We derive output fidelity and success probability for each, showing that the detection-based repetition code achieves the highest fidelity, while the [[4, 2, 2]] code provides better success rates. These results illustrate trade-offs between fidelity and yield, and highlight the potential of quantum codes in realistic noisy channels.

DOI
10.1109/icmic66299.2025.11257738

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This paper investigates entanglement distillation protocols assisted by quantum codes under bit-flip noise. Three protocols are compared: repetition code in correction and detection modes, and the [[4, 2, 2]] code in detection mode. We derive output fidelity and success probability for each, showing that the detection-based repetition code achieves the highest fidelity, while the [[4, 2, 2]] code provides better success rates. These results illustrate trade-offs between fidelity and yield, and highlight the potential of quantum codes in realistic noisy channels.
Quantum entanglement distillation refers to the process of extracting higher quality entangled pairs from a larger set of lower-quality pairs. Here, we present a basic structure of entanglement distillation protocol based on quantum error correction code. We perform the distillation procedure of this protocol in bit flip channel and show the performance in terms of output fidelity. Combining the characteristics of QEC and EDP, QEC-based EDP holds great promise for future applications in quantum network.
We study the performance of simple quantum error correcting codes with respect to correlated noise errors characterized by a finite correlation strength. Specifically, we consider bit flip (phase flip) noisy quantum memory channels and use repetition and noiseless quantum codes. We characterize the performance of the codes by means of the entanglement fidelity as function of the error probability and degree of memory. Finally, comparing the entanglement fidelities of repetition and noiseless quantum codes, we find a threshold for the correlation strength that allows to select the code with better performance.
Entanglement is essential for quantum information processing, but is limited by noise. We address this by developing high-yield entanglement distillation protocols with several advancements. (1) We extend the 2-to-1 recurrence entanglement distillation protocol to higher-rate n -to- ( n − 1 ) protocols that can correct any single-qubit errors. These protocols are evaluated through numerical simulations focusing on fidelity and yield. We also outline a method to adapt any classical error-correcting code for entanglement distillation, where the code can correct both bit-flip and phase-flip errors by incorporating Hadamard gates. (2) We propose a constant-depth decoder for stabilizer codes that transforms logical states into physical ones using single-qubit measurements. This decoder is applied to entanglement distillation protocols, reducing circuit depth and enabling protocols derived from high-performance quantum error-correcting codes. We demonstrate this by evaluating the circuit complexity for entanglement distillation protocols based on surface codes and quantum convolutional codes. (3) Our stabilizer entanglement distillation techniques advance quantum computing. We propose a fault-tolerant protocol for constant-depth encoding and decoding of arbitrary states in surface codes, with potential extensions to more general quantum low-density parity-check codes. This protocol is feasible with state-of-the-art reconfigurable atom arrays and surpasses the limits of conventional logarithmic depth encoders. Overall, our study integrates stabilizer formalism, measurement-based quantum computing, and entanglement distillation, advancing both quantum communication and computing.
Quantum Entanglement is a key to establish secure communication between two nodes in a communication channel. Ensuring high fidelity entanglement has always been a challenging task owing to interaction with the hostile channel environment. Several methods have been proposed in this paper to mitigate the problem. It has been shown that fidelity can be improved by encoding bell pairs using Quantum Repetition Codes (QRCs). In this regard, various QRC-based techniques are also analyzed mathematically, and their performances have been compared.
Realizing secure communication between distant parties is one of the main goals of quantum technology. Although quantum key distribution (QKD) promises information-theoretic security for sharing a secret key, the key rate heavily depends on the level of noise in the quantum channel. To overcome the noise, both quantum and classical techniques exist, i.e., entanglement distillation and classical advantage distillation. So far, these techniques have only been used separately from each other. Herein, we present a two-stage distillation scheme concatenating entanglement distillation with classical advantage distillation. For the advantage distillation, we utilize a fixed protocol, specifically, the repetition code; in the case of entanglement distillation, we employ an enumeration algorithm to find an optimal protocol. We test our scheme for noisy entangled states and demonstrate its quantitative advantage: Our two-stage distillation scheme achieves finite key rates even in a high-noise regime where entanglement distillation or advantage distillation alone cannot afford key sharing. We also calculate the security bounds for relevant QKD protocols with our key-distillation scheme and show that they exceed the previous security bounds on the critical quantum bit error rates with only advantage distillation. Since the advantage distillation part does not introduce further requirements for quantum resources other than those required for entanglement distillation, the proposed scheme is well suited for quantum key distribution tasks with entanglement distribution networks.
The goal of entanglement distillation is to turn a large number of weakly entangled states into a smaller number of highly entangled ones. Practical entanglement distillation schemes offer a trade-off between the fidelity to the target state and the probability of successful distillation. Exploiting such trade-offs is of interest in the design of quantum repeater protocols. Here, we present a number of methods to assess and optimize entanglement distillation schemes. We start by giving a numerical method to compute upper bounds on the maximum achievable fidelity for a desired probability of success. We show that this method performs well for many known examples by comparing it to well-known distillation protocols. This allows us to show optimality for many well-known distillation protocols for specific states of interest. As an example, we analytically prove optimality of the distillation protocol utilized within the Extreme Photon Loss entanglement generation scheme, even in the asymptotic limit. We proceed to present a numerical method that can improve an existing distillation scheme for a given input state, and we present an example for which this method finds an optimal distillation protocol. An implementation of our numerical methods is available as a Julia package.