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Secure Random Number Generation in Continuous Variable Systems

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Quantum Random Number Generation

Part of the book series: Quantum Science and Technology ((QST))

Abstract

Intrinsic uncertainty is a distinctive feature of quantum physics, which can be used to harness high-quality randomness. However, in realistic scenarios, the raw output of a quantum random-number generator (QRNG) is inevitably tainted by classical technical noise. The integrity of such a device can be compromised if this noise is tampered with, or even controlled by some malicious parties. In this chapter, we first briefly discuss how the quantum randomness can be characterised via information theoretic approaches, namely by quantifying the Shannon entropy and min-entropy. We then consider several ways where classical side-information can be taken into account via these quantities in a continuous-variable QRNG. Next, we focus on side-information independent randomness that is quantified by min-entropy conditioned on the classical noise. To this end, we present a method for maximizing the conditional min-entropy from a given quantum-to-classical-noise ratio. We demonstrate our approach on a vacuum state CV-QRNG. Lastly, we highlight several recent developments in the quest of developing secure CV-QRNG.

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Notes

  1. 1.

    The Rényi entropy is defined as \(H_{\alpha }(X)=\frac{1}{1-\alpha }\log _2\left[ \sum _{x_i \in X} P_X(x_i)^\alpha \right] \), with respect to a real-valued parameter \( \alpha \ge 0\). Min-entropy comes from taking the limit \(\alpha \rightarrow \infty \).

  2. 2.

    Here for brevity we omit the subscripts for the distributions.

  3. 3.

    SNR is defined as \(10\log _{10}(\sigma ^2_M/\sigma ^2_E)\), where M is the measurement signal and E is the noise.

  4. 4.

    Since the phase between the local oscillator and the vacuum field is arbitrary, it is therefore set as 0.

  5. 5.

    This can be done through an initial private random sequence, followed by recycling part of the generated random bits from the QRNG.

  6. 6.

    The generalization to account for the offset is detailed in Ref. [20].

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Authors and Affiliations

  1. Centre for Quantum Computation and Communication Technology, Department of Quantum Science, The Australian National University, Canberra, ACT, 2601, Australia

    Jing Yan Haw, Syed M. Assad & Ping Koy Lam

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  1. Jing Yan Haw
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  2. Syed M. Assad
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Correspondence to Jing Yan Haw .

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Editors and Affiliations

  1. Security and Communication Technologies, Center for Digital Safety and Security, AIT Austrian Institute of Technology GmbH, Klagenfurt, Austria

    Christian Kollmitzer

  2. Security and Communication Technologies, Center for Digital Safety and Security, AIT Austrian Institute of Technology GmbH, Klagenfurt, Austria

    Stefan Schauer

  3. Institute of Applied Informatics, Universität Klagenfurt, Klagenfurt, Austria

    Stefan Rass

  4. Security and Communication Technologies, Center for Digital Safety and Security, AIT Austrian Institute of Technology GmbH, Klagenfurt, Austria

    Benjamin Rainer

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Haw, J.Y., Assad, S.M., Lam, P.K. (2020). Secure Random Number Generation in Continuous Variable Systems. In: Kollmitzer, C., Schauer, S., Rass, S., Rainer, B. (eds) Quantum Random Number Generation. Quantum Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-72596-3_6

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