| Abstract |
Entangled quantum systems behave in ways impossible in any classical world. Even as entanglement of simple composite systems is reasonably well understood, the nature of complex entangled systems is largely unexplored. We will investigate entanglement of increasing complexity, either by entangling more and more systems with each other, or by entangling systems with a larger number of degrees of freedom. Firstly, we plan to derive new Bell's inequalities (tests of quantum non-locality) for higher-dimensional entangled systems and a larger number of choices for measurement settings for each system. The contradiction of quantum mechanical predictions with local realism is expected to be even stronger than currently known. Secondly, the entanglement that naturally exists between constituents of various complex physical systems such as chains of interacting spins will be studied. We will investigate how the amount of entanglement between several spins varies with the change of the number of spins, the strength of the coupling between them, temperature, the strength of the external field etc. The second part of the project investigates whether and how much entanglement is needed for quantum communication and quantum computation to outperform those which are based on the laws of classical physics. Firstly, we intend to develop new quantum communication complexity protocols exploiting higher-dimensional entanglement and to derive their complexity as a function of the amount of entanglement used. We expect to observe an increase of the separation between the complexity of the quantum solution and the best classical strategy as the dimensionality of the entangled systems grows. Secondly, by considering quantum computation as a communication process we plan to derive the complexity of certain quantum algorithms as a function of the amount of entanglement consumed.
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