Quantum Error Detection Based on Predefined Error Rates and Statistical Bounds

Öz

Reliable data transmission is a key challenge in quantum communication due to the inherent fragility of qubits and the probabilistic nature of quantum operations. In this study, we address this challenge by proposing a method tailored to environments where the quantum error rate is known in advance. Rather than relying on classical error correction strategies directly adapted to quantum systems, our approach introduces a mechanism that determines the optimal number of redundant transmissions based on a predefined threshold for success. By calculating how many times a qubit must be sent to achieve a desired probability of correctness, we offer a practical solution that can be used in scenarios with constrained quantum resources or in noisy quantum networks. The method focuses on improving reliability without the need for complex entanglement or syndromes, which may not be feasible in all experimental settings. Results show that this probabilistic redundancy model allows for an adjustable balance between communication cost and transmission success, offering flexibility based on system requirements. The approach is especially useful in early-stage quantum communication platforms where hardware limitations restrict the use of more advanced quantum error correction techniques.

Anahtar Kelimeler

• Quantum communication
• error rate
• reliable transmission
• quantum error handling

Önceden Belirlenmiş Hata Oranlarına ve İstatistiksel Sınırlara Dayalı Kuantum Hata Tespiti

Öz

Reliable data transmission is a key challenge in quantum communication due to the inherent fragility of qubits and the probabilistic nature of quantum operations. In this study, we address this challenge by proposing a method tailored to environments where the quantum error rate is known in advance. Rather than relying on classical error correction strategies directly adapted to quantum systems, our approach introduces a mechanism that determines the optimal number of redundant transmissions based on a predefined threshold for success. By calculating how many times a qubit must be sent to achieve a desired probability of correctness, we offer a practical solution that can be used in scenarios with constrained quantum resources or in noisy quantum networks. The method focuses on improving reliability without the need for complex entanglement or syndromes, which may not be feasible in all experimental settings. Results show that this probabilistic redundancy model allows for an adjustable balance between communication cost and transmission success, offering flexibility based on system requirements. The approach is especially useful in early-stage quantum communication platforms where hardware limitations restrict the use of more advanced quantum error correction techniques.

Anahtar Kelimeler

• Kuantum Hata Yönetimi
• Güvenilir İletim
• Hata Oranı
• Kuantum İletişimi

Kaynakça

1. [1] Nielsen, M.A., Chuang, I.L., “Quantum Computation and Quantum Information”, Cambridge University Press (2010).
2. [2] Bernhardt, C., “Quantum Computing for Everyone”, MIT Press (2020).
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4. [4] Wackerly, D., Mendenhall, W., Scheaffer, R.L., “Mathematical Statistics with Applications”, 6th ed., Duxbury Press (2007) : 460–491.
5. [5] Casella, G., Berger, R.L., “Statistical Inference”, 2nd ed., Duxbury (2002).
6. [6] Clopper, C.J., Pearson, E.S., “The Use of Confidence or Fiducial Limits Illustrated in the Case of the Binomial”, Biometrika 26(4) (1934) : 404–413.
7. [7] Agresti, A., Coull, B.A., “Approximate is Better than ‘Exact’ for Interval Estimation of Binomial Proportions”, The American Statistician 52(2) (1998) : 119–126.