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Quantum and semi-quantum lottery: strategies and advantages

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Abstract

Lottery is a game in which multiple players take chances in the hope of getting some rewards in cash or kind. In addition, from the time of the early civilizations, lottery has also been considered as an apposite method to allocate scarce resources. Technically, any scheme for lottery needs to be fair and secure, but none of the classical schemes for lottery are unconditionally secure and fair. As fairness demands complete unpredictability of the outcome of the lottery, it essentially requires perfect randomness. Quantum mechanics not only guarantees the generation of perfect randomness, it can also provide unconditional security. Motivated by these facts, a set of strategies for performing lottery using different type of quantum resources (e.g., single photon states, and entangled states) are proposed here, and it’s established that the proposed strategies lead to unconditionally secure and fair lottery schemes. A scheme for semi-quantum lottery that allows some classical users to participate in the lottery involving quantum resources is also proposed and the merits and demerits of all the proposed schemes are critically analysed. It is also established that the level of security is intrinsically related to the type of quantum resources being utilized. Further, it is shown that the proposed schemes can be experimentally realized using currently available technology, and that may herald a new era of commercial lottery.

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Notes

  1. \(\vert \psi ^{\pm } \rangle = \frac{1}{\sqrt{2}} \{ \vert 01 \rangle \pm \vert 10 \rangle \}\) and \(\vert \phi ^{\pm } \rangle = \frac{1}{\sqrt{2}} \{ \vert 00 \rangle \pm \vert 11 \rangle \}\)

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Acknowledgements

Authors thank Kishore Thapliyal and Abhishek Parakh for their feedback and interest in this work. Further, the authors acknowledge that this study is supported by the project “Partnership 2020: Leveraging US-India Cooperation in Higher Education to Harness Economic Opportunities and Innovation” which is enabling a collaboration between University of Nebraska at Omaha, and JIIT, Noida.

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  1. Jaypee Institute of Information Technology, A 10, Sector 62, Noida, UP, 201309, India

    Sandeep Mishra & Anirban Pathak

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  1. Sandeep Mishra
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Correspondence to Anirban Pathak.

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Mishra, S., Pathak, A. Quantum and semi-quantum lottery: strategies and advantages. Quantum Inf Process 22, 290 (2023). https://doi.org/10.1007/s11128-023-04041-x

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