Designing Optimal States and Transformations for Quantum Optical Metrology and Communication

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I will briefly describe our recent progress in solving some optimization problems involving metrology with multipath entangled photon states and optimization of quantum operations on such states. We found that in the problem of super-resolution phase measurement in the presence of a loss one can single out two distinct regimes: i) low-loss regime favoring purely quantum states akin the N00N states and ii) high-loss regime where generalized coherent states become the optimal ones. Next I will describe how to optimize photon-entangling operations beyond the Knill-Laflamme-Milburn scheme and, in particular, how to exploit hyperentangled states for entanglement-assisted error correction.If time allows I will briefly review our results on generalization of the Bloch Sphere for the case of two qubits exploiting the SU(4)/Z2-SO(6) group isomorphism. References 1. D. Uskov & Jonathan P. Dowling. Quantum Optical Metrology in the Presence of a Loss (in preparation); Sean D. Huver et al, Entangled Fock States for Robust Quantum Optical Metrology, Imaging, and Sensing, arXiv:0808.1926. 2. D. Uskov et al, Maximal Success Probabilities of Linear-Optical Quantum Gates, arXiv:0808.1926. 3. M. Wilde and D. Uskov, Linear-Optical Hyperentanglement-Assisted Quantum Error-Correcting Code, arXiv:0807.4906. 4. D. Uskov and R. Rau Geometric phases and Bloch sphere constructions for SU(N), with a complete description of SU(4), Phys. Rev. A 78, 022331 (2008).