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Applications of Semidefinite Programming in Quantum Cryptography

Coin-flipping is the cryptographic task of generating a random coin-flip between two mistrustful parties. Kitaev discovered that the security of quantum coin-flipping protocols can be analyzed using semidefinite programming. This lead to his result that one party can force a desired coin-flip outcome with probability at least 1/√2.

We give sufficient background in quantum computing and semidefinite programming to understand Kitaev's semidefinite programming formulation for coin-flipping cheating strategies. These ideas are specialized to a specific class of protocols singled out by Nayak and Shor. We also use semidefinite programming to solve for the maximum cheating probability of a particular protocol which has the best known security.

Furthermore, we present a family of protocols where one party has a greater probability of forcing an outcome of 0 than an outcome of 1. We also discuss a computer search to find specific protocols which minimize the maximum cheating probability.
Date January 2007
CreatorsSikora, Jamie William Jonathon
Source SetsUniversity of Waterloo Electronic Theses Repository
Detected LanguageEnglish
TypeThesis or Dissertation
Format659000 bytes, application/pdf

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