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Abstract Two‐way quantum key distribution (QKD) protocols utilize bi‐directional quantum communication to establish a shared secret key. Due to the increased attack surface, security analyses remain challenging. Here a high‐dimensional variant of the Ping Pong protocol is investigated and an information theoretic security analysis in the finite‐key setting is performed. The main contribution in this work is to show a new proof methodology for two‐way quantum key distribution protocols based on the quantum sampling framework of Bouman and Fehr introduced in 2010 and also sampling‐based entropic uncertainty relations introduced by the authors in 2019. The Ping Pong protocol is only investigated here, but these methods may be broadly applicable to other QKD protocols, especially those relying on two‐way channels. Along the way, some fascinating benefits to high‐dimensional quantum states applied to two‐way quantum communication are also showed.
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A cyclotomic family of thin hypergeometric monodromy groups in $${\text {Sp}}_4({\mathbb {R}})$$
We exhibit an infinite family of discrete subgroups of Sp4 (R) which have a number of remarkable properties. Our results are established by showing that each group plays ping-pong on an appropriate set of cones. The groups arise as the monodromy of hypergeometric differential equations. Additionally, we relate the cones used for ping-pong in R4 with crooked surfaces, which we then use to exhibit domains of discontinuity for the monodromy groups in the Lagrangian Grassmannian. These domains of discontinuity lead to uniformizations of variations of Hodge structure with Hodge numbers (1, 1, 1, 1).
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- PAR ID:
- 10515742
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Geometriae Dedicata
- Volume:
- 218
- Issue:
- 2
- ISSN:
- 0046-5755
- Page Range / eLocation ID:
- Paper No. 44, 53
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s10711-024-00893-4
