2011/02/09 by Marcin Zwierz, Zwierz, Marcin
Physics and Astronomy · Computer Science · #Quantum Mechanics and Applications #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography
paper · pdf · doi:10.48550/arxiv.1102.1918
This thesis presents three different results in quantum information theory.\nThe first result addresses the theoretical foundations of quantum metrology.\nThe Heisenberg limit considered as the ultimate limit in quantum metrology sets\na lower bound on how precisely a physical quantity can be measured given a\ncertain amount of resources in any possible measurement. Recently, however,\nseveral measurement procedures have been proposed in which the Heisenberg limit\nseemed to be surpassed. This led to an extensive debate over the question how\nthe sensitivity scales with the physical resources and the computational\nresources that are used in estimation procedures. Here, we reconcile the\nphysical definition of the relevant resources with the information-theoretical\nscaling in terms of the query complexity of a quantum network. This leads to a\nnovel and ultimate Heisenberg limit that applies to all conceivable measurement\nprocedures. The second result reveals a close relationship between quantum\nmetrology and the Deutsch-Jozsa algorithm over continuous-variable quantum\nsystems. Here, we develop a general procedure, characterized by two parameters,\nthat unifies parameter estimation and the Deutsch-Jozsa algorithm. The\nprocedure estimates a value of an unknown parameter with Heisenberg-limited\nprecision or solves the Deutsch-Jozsa problem in a single run without the use\nof any entanglement. The third result illustrates how physical principles that\ngovern interaction of light and matter can be efficiently employed to create a\ncomputational resource for a (one-way) quantum computer. More specifically, we\ndemonstrate theoretically a scheme based on atomic ensembles and the dipole\nblockade mechanism for generation of the so-called cluster states in a single\nstep. This procedure is significantly more efficient than any known robust\nprobabilistic entangling operation.\n