A bound on the quantum value of all compiled nonlocal games

Fuente: arXiv
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Main Authors: Kulpe, Alexander, Malavolta, Giulio, Paddock, Connor, Schmidt, Simon, Walter, Michael
Format: Preprint
Published: 2024
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author Kulpe, Alexander
Malavolta, Giulio
Paddock, Connor
Schmidt, Simon
Walter, Michael
author_facet Kulpe, Alexander
Malavolta, Giulio
Paddock, Connor
Schmidt, Simon
Walter, Michael
contents A cryptographic compiler introduced by Kalai et al. (STOC'23) converts any nonlocal game into an interactive protocol with a single computationally bounded prover. Although the compiler is known to be sound in the case of classical provers and complete in the quantum case, quantum soundness has so far only been established for special classes of games. In this work, we establish a quantum soundness result for all compiled two-player nonlocal games. In particular, we prove that the quantum commuting operator value of the underlying nonlocal game is an upper bound on the quantum value of the compiled game. Our result employs techniques from operator algebras in a computational and cryptographic setting to establish information-theoretic objects in the asymptotic limit of the security parameter. It further relies on a sequential characterization of quantum commuting operator correlations which may be of independent interest.
format Preprint
id arxiv_https___arxiv_org_abs_2408_06711
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A bound on the quantum value of all compiled nonlocal games
Kulpe, Alexander
Malavolta, Giulio
Paddock, Connor
Schmidt, Simon
Walter, Michael
Quantum Physics
Cryptography and Security
Mathematical Physics
A cryptographic compiler introduced by Kalai et al. (STOC'23) converts any nonlocal game into an interactive protocol with a single computationally bounded prover. Although the compiler is known to be sound in the case of classical provers and complete in the quantum case, quantum soundness has so far only been established for special classes of games. In this work, we establish a quantum soundness result for all compiled two-player nonlocal games. In particular, we prove that the quantum commuting operator value of the underlying nonlocal game is an upper bound on the quantum value of the compiled game. Our result employs techniques from operator algebras in a computational and cryptographic setting to establish information-theoretic objects in the asymptotic limit of the security parameter. It further relies on a sequential characterization of quantum commuting operator correlations which may be of independent interest.
title A bound on the quantum value of all compiled nonlocal games
topic Quantum Physics
Cryptography and Security
Mathematical Physics
url https://arxiv.org/abs/2408.06711