  We introduce a definition of the fidelity function for multi-round quantum
strategies, which we call the strategy fidelity, that is a generalization of
the fidelity function for quantum states. We provide many properties of the
strategy fidelity including a Fuchs-van de Graaf relationship with the strategy
norm. We also provide a general monotinicity result for both the strategy
fidelity and strategy norm under the actions of strategy-to-strategy linear
maps. We illustrate an operational interpretation of the strategy fidelity in
the spirit of Uhlmann's Theorem and discuss its application to the security
analysis of quantum protocols for interactive cryptographic tasks such as
bit-commitment and oblivious string transfer. Our analysis is general in the
sense that the actions of the protocol need not be fully specified, which is in
stark contrast to most other security proofs. Lastly, we provide a semidefinite
programming formulation of the strategy fidelity.
