Quantum multiparameter estimation with graph states

TL;DR

This paper proposes a scheme for quantum multiparameter estimation using graph states within SU(N) dynamics, demonstrating enhanced precision beyond classical limits and establishing graph states as optimal resources in quantum metrology.

Contribution

It introduces a novel multiparameter estimation scheme with graph states in SU(N) dynamics, showing precision improvements and optimal measurement strategies.

Findings

Global estimation precision exceeds local estimation.

Precision of simultaneous parameters matches single-parameter estimation.

Graph states are proven to be optimal for quantum metrology.

Abstract

In the SU(2) dynamics, it is especially significant to achieve a simultaneous optimal multiparameter estimation but it is very difficult. Evolution on SU(N) dynamics is a research method to explore simultaneous multiparameter estimation with the quantum network. As the highly entangled states, graph state, is an intrinsical quantum resource for quantum metrology. For n-qubit graph state, we propose a simultaneous multiparameter estimation scheme that investigates evolution in SU(N) dynamics. For single-parameter estimation, the precision limit beyond the Heisenberg limit in the higher dimension spin of SU(2). We consider two scenarios where the Hamiltonian operator is commutation and non-commutation respectively and verify that the global estimation precision is higher than the local estimation precision. In the parameter limit condition, the precision of parameter estimation for the simultaneous estimation of each parameter is equal to the precision of the singleparameter estimation. In addition, we find a precision-enhancement scheme that depends on the dynamics SU(N). The smaller the N for the dynamics evolution, the higher the precision of the parameter estimation. Finally, we prove that the graph state is the optimal state of quantum metrology, a set of optimal measurement basic can be found, and the precision limit of multiparameter estimation can attain the quantum Cram\'er-Rao bound.