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arXiv:0910.1910 · Physical Review A

Experimental estimation of one-parameter qubit gates in the presence of phase diffusion

Davide Brivio, S. Cialdi, Stefano Vezzoli, Berihu Teklu, Marco G. Genoni, Stefano Olivares, Matteo G. A. Paris

Published Jan 7, 2010• 103 citations
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Abstract

We address estimation of one-parameter qubit gates in the presence of phase diffusion. We evaluate the ultimate quantum limits to precision, seek optimal probes and measurements, and demonstrate an optimal estimation scheme for polarization encoded optical qubits. An adaptive method to achieve optimal estimation in any working regime is also analyzed in detail and experimentally implemented.

DOI
10.1103/physreva.81.012305

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We address the estimation of phase-shifts for qubit systems in the presence of noise. Different sources of noise are considered including bit flip, bit-phase flip and phase flip. We derive the ultimate quantum limits to precision of estimation by evaluating the analytical expressions of the quantum Fisher information and assess performances of feasible measurements by evaluating the Fisher information for realistic spin-like measurements. We also propose an experimental scheme to test our results.
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Coherent ensembles of NNN qubits present an advantage in quantum phase estimation over separable mixtures, but coherence decay due to classical phase diffusion reduces overall precision. In some contexts, the strength of diffusion may be the parameter of interest. We examine estimation of both phase and diffusion in large spin systems using a novel mathematical formulation. For the first time, we show a closed form expression for the quantum Fisher information for estimation of a unitary parameter in a noisy environment. The optimal probe state has a non-Gaussian profile and differs also from the canonical phase state; it saturates a new tight precision bound. For noise below a critical threshold, entanglement always leads to enhanced precision, but the shot-noise limit is beaten only by a constant factor, independent of NNN. We provide upper and lower bounds to this factor, valid in low and high noise regimes. Unlike other noise types, it is shown for N≫1N \gg 1N≫1 that phase and diffusion can be measured simultaneously and optimally.