Fidelity of Quantum Strategies with Applications to Cryptography * † 1 Introduction 1.1 Review of quantum strategies

Gus Gutoski, Ansis Rosmanis, Jamie Sikora
1998 Phys-ical Sciences and Engineering CC-BY 12th Conference on the Theory of Quantum Computation, Communication, and Cryptography   unpublished
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 interesting properties of the strategy fidelity including a Fuchs-van de Graaf relationship with the strategy norm. 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
more » ... ols for interactive cryptographic tasks such as bit-commitment and oblivious string transfer. Our analysis is very 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. In this paper we consider multiple-round interactions between two parties involving the exchange of quantum information. There is a natural asymmetry between the parties as only one of the parties can send the first message or receive the final message. Since we are not