Perfect Commuting-Operator Strategies for Linear System Games
Perfect Commuting-Operator Strategies for Linear System Games
复制标题
线性系统博弈的完美通勤运营商策略
DOI：
10.1063/1.4973422
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
William Slofstra
中科院分区：
文献类型：
--
作者：
R. Cleve;Li Liu;William Slofstra
线性系统博弈是 Cleve 和 Mittal 提出的 Mermin 魔方博弈的推广。他们表明，纠缠张量积模型中线性系统博弈的完美策略对应于一组特定非交换方程的有限维算子解。我们研究了纠缠的通勤算子模型中的线性系统博弈，其中 Alice 和 Bob 的测量算子作用于联合希尔伯特空间，并且 Alice 的算子必须与 Bob 的算子进行通勤。我们表明，该模型中的完美策略对应于非交换方程的可能无限维算子解。证明基于与由非交换方程产生的线性系统相关的有限呈现群。
Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly-infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely-presented group associated to the linear system which arises from the non-commutative equations.
影响因子：
1.7
作者：
V. Paulsen;S. Severini;D. Stahlke;I. Todorov;A. Winter
通讯作者：
V. Paulsen;S. Severini;D. Stahlke;I. Todorov;A. Winter