Winning Rates of $(n,k)$ Quantum Coset Monogamy Games
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918151097155584 |
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| author | Schleppy, Michael Soljanin, Emina |
| author_facet | Schleppy, Michael Soljanin, Emina |
| contents | 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 $R=\frac{k}{n}\in [0,1]$. This bound improves upon previous results for the case of $R=1/2$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17736 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Winning Rates of $(n,k)$ Quantum Coset Monogamy Games Schleppy, Michael Soljanin, Emina Quantum Physics Information Theory 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 $R=\frac{k}{n}\in [0,1]$. This bound improves upon previous results for the case of $R=1/2$. 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. |
| title | Winning Rates of $(n,k)$ Quantum Coset Monogamy Games |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2501.17736 |