to characterize the effect and illustrate how to optimize observables to attain a bound with limited accessibility of observables. In addition, we introduce the minimum Euclidean distance to quantify the difference between an observable and the optimal ones in terms of the Frobenius norm and find that the measurement with a shorter distance to the optimal ones benefits the estimation. Two examples are presented to show our theory. In the first, we analyze the effect of nonoptimal measurement on the estimation precision of the transition frequency for a driven qubit. In the second example, we consider a bipartite system, in which one of them is measurement inaccessible. To be specific, we take a toy model, the nitrogen-vacancy (NV) center in diamond, as the bipartite system, where the NV-center electronic spin interacts with a single nucleus via the dipole-dipole interaction. We achieve a precise estimation for the nuclear Larmor frequency by optimizing only the observables of the electronic spin. In these two examples, the minimum Euclidean distance between an observable and the optimal ones is analyzed and the results show that the closer the observable to the optimal ones the better the estimation precision. This paper establishes a relation between the estimation precision and the distance of the nonoptimal observable to the optimal ones, which could be helpful for experiments seeking the best observable in parameter estimation.

DOI: 10.1103/physreva.109.032215

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State Preparation and Metrology of Nitrogen Nuclear Spin in Diamond

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The nitrogen vacancy center in internal and external fields

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By using two NVs with a distance of less then 20 nm, a demonstration of nanoscale single fundamental charge detection was feasible. Here one NV was used as a controllable fundamental charge while the other NV was used as sensor NV, detecting the electric field of the fundamental charge. This allowed for the detection of a single electronic charge at ambient conditions. Another keystone of quantum technology is the reliable on demand or heralded creation of entanglement. In this dissertation, the successful entanglement of two electron spins in solid state at ambient conditions is demonstrated. The fundamental interaction used to create an entangled state was dipolar coupling between the two electron spins. In order to be able to harness weaker coupling strengths, an entanglement protocol based on dynamical decoupling was developed. A fidelity of F=0.67±0.04 was demonstrated. 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Jan 1, 20142 citations

Optimal quantum multiparameter estimation and application to dipole- and exchange-coupled qubits

Kevin C Young, Mohan Sarovar, Robert L. Kosut +1 more

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arXiv:0812.4635Physical Review AJun 2, 200935 citations

\mathrm{\ensuremath{\Lambda}}

(\mathcal{PT})

-symmetric non-Hermitian Hamiltonian and give the optimal measurement. Surprisingly, we find some interesting properties of this

\mathcal{PT}

-symmetric Hamiltonian QFI, such as the mutations in QFI at exceptional point. Moreover, we also compare the variance of estimation generated by the optimal measurement with the theoretical precision bound to verify the condition for optimal measurements we proposed.