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Resources and decoherence in qubit metrology

Anil Shaji, University of New Mexico

(Session 12 : Sunday from 11:15-11:45)

Abstract. In quantum parameter estimation, accuracies that beat the standard quantum limit can be obtained by using the quantum properties of the probes and by modulating the nature of the interaction between the probe and the measured system. When qubits are used to construct a quantum probe, it is known that initializing n qubits in an entangled state, rather than in a separable state, can improve the measurement uncertainty by a factor of $1/\\sqrt{n}$. It is also known that if the interaction between the probe and the measured system involves $k$-qubit couplings then the best possible scaling of the measurement uncertainty is $1/n^k$ for a probe initialized in an entangled state and $1/n^{k-1/2}$ for a probe initialized in a product state. We investigate how the measurement uncertainty is affected when the individual qubits in a probe are subjected to decoherence in measurement schemes involving both linear and nonlinear couplings. In the face of such decoherence, we regard the rate $R$ at which qubits can be generated and the total duration $\\tau$ of a measurement as fixed resources, and we determine the optimal use of entanglement among the qubits and the resulting optimal measurement uncertainty as functions of $R$ and $\\tau$.