Quantum Strategies and Local Operations

Understand

This thesis is divided into two parts.

• In Part I we introduce a new formalism for quantum strategies, which specify the actions of one party in any multi-party interaction involving the exchange of multiple quantum messages among the parties.
• This formalism associates with each strategy a single positive semidefinite operator acting only upon the tensor product of the input and output message spaces for the strategy.
• We establish three fundamental properties of this new representation for quantum strategies and we list several applications, including a quantum version of von Neumann's celebrated 1928 Min-Max Theorem for zero-sum games and an efficient algorithm for computing the value of such a game.