The Fisher information $F$ gives a limit to the ultimate precision achievable
in a phase estimation protocol. It has been shown recently that the Fisher
information for a linear two-mode interferometer cannot exceed the number of
particles if the input state is separable. As a direct consequence, with such
input states the shot-noise limit is the ultimate limit of precision. In this
work, we go a step further by deducing bounds on $F$ for several multiparticle
entanglement classes. These bounds imply that genuine multiparticle
entanglement is needed for reaching the highest sensitivities in quantum
interferometry. We further compute similar bounds on the average Fisher
information $\bar F$ for collective spin operators, where the average is
performed over all possible spin directions. We show that these criteria detect
different sets of states and illustrate their strengths by considering several
examples, also using experimental data. In particular, the criterion based on
$\bar F$ is able to detect certain bound entangled states.Comment: Published version. Notice also the following article [Phys. Rev. A
85, 022322 (2012), DOI: 10.1103/PhysRevA.85.022322] by Geza T\'oth on the
same subjec
We present a scalable method for the tomography of large multiqubit quantum registers. It acquires information about the permutationally invariant part of the density operator, which is a good approximation to the true state in many relevant cases. Our method gives the best measurement strategy to minimize the experimental effort as well as the uncertainties of the reconstructed density matrix. We apply our method to the experimental tomography of a photonic four-qubit symmetric Dicke state.
Common tools for obtaining physical density matrices in experimental quantum state tomography are shown here to cause systematic errors. For example, using maximum likelihood or least squares optimization for state reconstruction, we observe a systematic underestimation of the fidelity and an overestimation of entanglement. A solution for this problem can be achieved by a linear evaluation of the data yielding reliable and computational simple bounds including error bars.
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