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研究生： 陳又加
Chen, Yu-chia
論文名稱： 可攜式量子亂數產生器
Portable Quantum Random Number Generator
指導教授： 李瑞光
Lee, Ray-Kuang
口試委員: 李明昌
賴青沂
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 光電工程研究所
Institute of Photonics Technologies
論文出版年： 2025
畢業學年度： 113
語文別： 英文
論文頁數： 28
中文關鍵詞： 真空態 、亂數 、量子藝術
外文關鍵詞： balanced homodyne detector, Toeplitz hashing, NIST test, quantum art
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    • 最簡單在確定性算法的基礎上改成可以得出隨機結果的方式即是使用亂數，
    因此擁有良好的亂數產生器是保證眾多仰賴隨機結果的應用之基石，例如產生
    電子金鑰、數位抽獎、模擬計算。現今主要使用的亂數產生器，其亂數來源多
    為熱擾動或複雜的渾沌系統，這些系統並非物理上不可預測，其產出亂數可能
    有週期性或可藉由強大的計算能力來預知結果。
    量子亂數產生器其亂數來源如名稱所示是以量子系統為其亂數來源的亂數產
    生器，其不可預測性是源自於其量子物理的機率性質，因此量子亂數產生器能
    防範一般亂數產生器所面臨的問題。
    本文以光纖系統量測真空態來作為量子亂數產生器的亂數來源，並使用單板
    電腦來做後處理來實現可攜帶式量子亂數產生器，並且我們與清華大學科技藝
    術研究所的藝術家們合作，以我們的可攜帶式量子亂數產生器為中心，舉辦藝
    術展演。本文最後會對產出的亂數進行檢驗，以確認其是否可靠的產出亂數，
    並且對真空態為亂數來源的量子亂輸產生器進行討論。

    For an deterministic algorithm, the simplest way to have random result is in-
    troducing random numbers into the process. Therefore a good random number
    generator is the cornerstone for application built upon random outcome, e.g., dig-
    ital key, computer lottery, and simulation computation. Most random number
    generators we use day to day use random source base on thermal fluctuation or
    complicated chaotic system, which are not unpredictable in nature, so one could
    foresee the result by exploiting its periodicity or brute forcing with gigantic com-
    putational power.
    Quantum random number generator is a kind of random number generator us-
    ing quantum phenomenon as random source. The unpredictable characteristic of
    the signal is derived from the probabilistic nature of quantum physics. In essence,
    quantum random number generator can prevent problems of generic random num-
    ber generator.
    In this article, we construct a portable quantum random number generator,
    which uses measurement of vacuum state of a fiber optic system as random source,
    and Raspberry Pi to compute the post processing. We also collaborate with artists
    from Graduate Institute of Art and Technology National Tsing Hua University to
    hold an art exhibition around our portable quantum random number generator.The
    last part of this article is about testing the random number sequence from our
    portable QRNG to verify the outcome is reliable or not and discussion of QRNG
    based on measurement of vacuum state.

    Contents Abstract (Chinese) I Abstract II Acknowledgements (Chinese) III Acknowledgements IV Contents V List of Figures VIII List of Tables IX 1 Introduction 1 1.1 Random number generator . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Project objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3.1 Hardware structure . . . . . . . . . . . . . . . . . . . . . . . 2 1.3.2 Software function . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Terminology 4 2.1 Randomness source . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Vacuum state . . . . . . . . . . . . . . . . . . . . . . . . . . 4 V 2.1.2 Dark noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.4 CMRR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Post processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 Toeplitz hashing . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.2 Min-entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Randomness test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3.1 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3.2 NIST test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 Construct method 10 3.1 Hardware component . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.1.1 Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.1.2 Coupler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.1.3 Balanced homodyne detector . . . . . . . . . . . . . . . . . . 11 3.1.4 Amp&ADC . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.5 Single-board computer . . . . . . . . . . . . . . . . . . . . . 11 3.2 Function for post-processing . . . . . . . . . . . . . . . . . . . . . . 12 3.2.1 Read input . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2.2 Gaussian fitting . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2.3 Min-entropy calculation . . . . . . . . . . . . . . . . . . . . 13 3.2.4 Toeplitz hashing . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3 Function for deployment . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3.1 Laser control via VirtualHere . . . . . . . . . . . . . . . . . 15 3.3.2 Threading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.4 Post-processing procedure . . . . . . . . . . . . . . . . . . . . . . . 16 VI 4 Result testing 17 4.1 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.1.1 Calculation method of autocorrelation . . . . . . . . . . . . 17 4.1.2 Result plot . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 NIST test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5 Discussion 21 5.1 Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.2 Bottleneck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Bibliography 27

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