Winning Rates of (n, k) Quantum Coset Monogamy Games

Schleppy, Michael; Soljanin, Emina

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https://hdl.handle.net/2142/130327 Copy

Description

Title

Winning Rates of (n, k) Quantum Coset Monogamy Games

Author(s)

• Schleppy, Michael
• Soljanin, Emina

Issue Date

2025-09-17

Keyword(s)

• Quantum correlations
• Quantum games
• Coset states
• Subspace states
• Monogamy-of-entanglement
• Subspace permutations

Abstract

We formulate the (n, k) Coset Monogamy Game, in which two players must extract complementary information of unequal size (k bits vs. n − k bits) from a random coset state without communicating. The complementary information takes the form of random Pauli-X and Pauli-Z errors on subspace states. Our game generalizes those considered in previous works that deal with the case of equal information size (k = n/2). We prove a convex upper bound of the information-theoretic winning rate of the (n, k) Coset Monogamy Game in terms of the subspace rate R = k/n ∈ [0, 1]. This bound improves upon previous results for the case of R = 1/2, in part due to a structural result we prove on subspace permutations, which may have broader combinatorial interest. We also prove the achievability of an optimal winning probability upper bound for the class of unentangled strategies of the (n, k) Coset Monogamy Game.

Publisher

Allerton Conference on Communication, Control, and Computing

Series/Report Name or Number

2025 61st Allerton Conference on Communication, Control, and Computing Proceedings

ISSN

2836-4503

Type of Resource

Text

Genre of Resource

Conference Paper/Presentation

Language

eng

Handle URL

https://hdl.handle.net/2142/130327&&

Copyright and License Information

Copyright 2025 is held by Michael Schleppy and Emina Soljanin.

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