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Simultaneous Haar Indistinguishability with Applications to Unclonable Cryptography

Authors Prabhanjan Ananth , Fatih Kaleoglu, Henry Yuen

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Author Details

Prabhanjan Ananth
  • University of California, Santa Barbara, CA, USA
Fatih Kaleoglu
  • University of California, Santa Barbara, CA, USA
Henry Yuen
  • Columbia University, New York, NY, USA

Funding

  • Ananth, Prabhanjan: the National Science Foundation Grant No. 2329938.
  • Kaleoglu, Fatih: the National Science Foundation Grant No. 2329938.
  • Yuen, Henry: AFOSR awards FA9550-21-1-0040 and FA9550-23-1-0363, NSF CAREER award CCF-2144219, NSF award CCF-2329939, and the Sloan Foundation.

Acknowledgements

The authors would like to thank Ludovico Lami for answering many questions related to non-local state discrimination.

Cite As Get BibTex

Prabhanjan Ananth, Fatih Kaleoglu, and Henry Yuen. Simultaneous Haar Indistinguishability with Applications to Unclonable Cryptography. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 7:1-7:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.7

Abstract

We study a novel question about nonlocal quantum state discrimination: how well can non-communicating - but entangled - players distinguish between different distributions over quantum states? We call this task simultaneous state indistinguishability. Our main technical result is to show that the players cannot distinguish between each player receiving independently-chosen Haar random states versus all players receiving the same Haar random state.
We show that this question has implications to unclonable cryptography, which leverages the no-cloning principle to build cryptographic primitives that are classically impossible to achieve. Understanding the feasibility of unclonable encryption, one of the key unclonable primitives, satisfying indistinguishability security in the plain model has been a major open question in the area. So far, the existing constructions of unclonable encryption are either in the quantum random oracle model or are based on new conjectures.
We leverage our main result to present the first construction of unclonable encryption satisfying indistinguishability security, with quantum decryption keys, in the plain model. We also show other implications to single-decryptor encryption and leakage-resilient secret sharing. These applications present evidence that simultaneous Haar indistinguishability could be useful in quantum cryptography.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic protocols
  • Theory of computation → Quantum information theory
Keywords
  • Quantum
  • Haar
  • unclonable encryption

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