Metrological Characterization of Non-Gaussian Entangled States of Superconducting Qubits

Abstract

Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterizes the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalization of the RSP with respect to nonlinear observables, and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, we report the characterization of multiparticle entangled states generated during its nonlinear dynamics. First, selecting 10 qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89 +0.28 −0.29 dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.

Squeezing of nonlinear spin observables by one axis twisting in the presence of decoherence: An analytical study

“…As shown above, the evolution with the one-axis twisting Hamiltonian, used as a system preparation before phase imprinting, allows to achieve a high metrological gain through the squeezing of nonlinear spin observables. Such observables, that are higher moments of the spin components, can be extracted from the statistics of linear spin observables [34][35][36][37]41]. However, due to the increased measurement time and the need for low detection noise, this is challenging to achieve in systems with large atom numbers.…”

“…A promising alternative is provided by over-squeezed spin states [34][35][36][37] that are generated by OAT after the linear squeezing time but on time scales that are shorter than those needed to reach Heisenberg scaling. The sensitivity of these states cannot be captured in terms of the squeezing of linear spin observables, but instead requires the measurement of nonlinear spin observables [38] whose squeezing can lead to significant quantum enhancements beyond the reach of linear spin squeezing.…”

Relative phase distribution and the precision of optical phase sensing in quantum metrology

“…But perhaps the most prominent application of photonic quantum metrology so far has been the improvement of * saldanha@fisica.ufmg.br the sensitivity of gravitational wave detectors [19][20][21][22]. It is worth mentioning that many other physical systems, besides quantum light, are used in the broader area of quantum metrology [23][24][25].…”

Experimental demonstration of topological bounds in quantum metrology

“…Specifically, the precision limit for single parameter estimation is given by the quantum Cramér-Rao bound (CRB) [1], which relates the smallest achievable variance of an unbiased estimator to the inverse of the QFI of the underlying state. The QFI was measured in various experiments by using different methods [16][17][18][19][20][21]. While recent experiments tested and verified the CRB through QFI measurements in the context of single-parameter-evaluation schemes [21], the extension to multi-parameter scenarios is generally more complex due to the possible incompatibility of optimal quantum measurements targeting each parameter [22][23][24][25][26][27][28][29][30][31][32].…”