Nonlocality & Communication Complexity

This thesis discusses the connection between the nonlocal b eh vior of quantum mechanics and the communication complexity of distributed co mputations. The first three chapters provide an introduction to quantum information th eory with an emphasis on the description of entangled systems. The next chapter look s at how to measure the complexity of distributed computations. This is expressed by the ‘communication complexity’, defined as the minimum amount of communication req uired for the evaluation of a function —a communication necessary because the input strings and are distributed over separated parties. In the theory of qua ntum communication, we try to use the nonlocal effects of entangled quantum bits to redu c communication complexity. In chapters 5, 6 and 7, such an improvement over clas sic l communication is indeed established for various functions. However, it is al so shown that entanglement does not lead to a more efficient calculation of the inner prod uct function. We thus reach the conclusion that nonlocality sometimes—but not al ways—allows a reduction in communication complexity. This subtle relationship bet w en nonlocality and communication vanishes when we consider ‘superstrong’ correl ations. We demonstrate that if a violation of the Clauser-Horne-Shimony-Holt inequali ty with the maximum factor of is assumed, all decision problems have the same trivial comp lexity of a single bit. The thesis concludes with an overview of the current status o f quantum communication theory, and a discussion of the experimental feasability of he suggested protocols.