Finite-Size Security Bounds in Semi-Quantum Key Distribution: Spectral, Operator-Theoretic, and Entropic Perspectives
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912633076056064 |
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| author | Ratul, Zahidur Rezwan |
| author_facet | Ratul, Zahidur Rezwan |
| contents | We study Semi-Quantum Key Distribution (SQKD) with a focus on finite-size security bounds, developed through three complementary perspectives. (i) Spectral disturbance: wrong-basis Lüders updates produce closed-form spectra and purity loss, which serve as basis-independent indicators of disturbance. (ii) Operator-theoretic reduction: in Z/Z-sifted rounds, intercept-resend attacks can be represented as an effective depolarizing channel, characterized by a fidelity-QBER relation. (iii) Entropic trade-offs: Maassen-Uffink and memory-assisted uncertainty relations certify security through X tests and reflection rounds, even when the sifted QBER is low. The exposition provides step-by-step derivations supported by physically interpretable figures, and the framework concludes with finite-size estimates based on concentration inequalities that are suited for practical parameter estimation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_25078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite-Size Security Bounds in Semi-Quantum Key Distribution: Spectral, Operator-Theoretic, and Entropic Perspectives Ratul, Zahidur Rezwan Quantum Physics 81P94, 94A60, 68Q12 E.3; F.1.2; K.6.5 We study Semi-Quantum Key Distribution (SQKD) with a focus on finite-size security bounds, developed through three complementary perspectives. (i) Spectral disturbance: wrong-basis Lüders updates produce closed-form spectra and purity loss, which serve as basis-independent indicators of disturbance. (ii) Operator-theoretic reduction: in Z/Z-sifted rounds, intercept-resend attacks can be represented as an effective depolarizing channel, characterized by a fidelity-QBER relation. (iii) Entropic trade-offs: Maassen-Uffink and memory-assisted uncertainty relations certify security through X tests and reflection rounds, even when the sifted QBER is low. The exposition provides step-by-step derivations supported by physically interpretable figures, and the framework concludes with finite-size estimates based on concentration inequalities that are suited for practical parameter estimation. |
| title | Finite-Size Security Bounds in Semi-Quantum Key Distribution: Spectral, Operator-Theoretic, and Entropic Perspectives |
| topic | Quantum Physics 81P94, 94A60, 68Q12 E.3; F.1.2; K.6.5 |
| url | https://arxiv.org/abs/2509.25078 |