Quantum metrology harnesses entanglement to improve measurement precision beyond classical limits. While standard protocols rely on two-level qubits to estimate a single parameter, extending them to entangled multi-level qudits enables the optimal simultaneous estimation of multiple parameters within a single probe. However, generating such multi-level entanglement and harnessing it for joint multi-parameter estimation in atomic clocks has remained an outstanding challenge. Here, we experimentally demonstrate genuine qutrit entanglement and joint multi-parameter estimation in an optical clock platform. Leveraging control over the ground state and two fine-structure clock states of $^{88}\text{Sr}$ atoms trapped in triple-magic optical tweezers, we generate a maximally entangled two-qutrit state with a loss-postselected fidelity of F = 0.85(1), certifying genuine multi-level entanglement. Taking advantage of this high-dimensional entanglement, we theoretically construct and experimentally realize an optimal two-qutrit metrological probe state and noise-robust readout circuit to simultaneously estimate injected phases on two optical clock transitions. We observe a joint estimation variance below the ideal individual two-level sensing threshold, and show theoretically that this advantage persists at state-of-the-art atom numbers under circuit-level noise. These results demonstrate the key building blocks towards quantum information science with high-dimensional states encoded in the internal energy levels of neutral atoms.
Ohad Lib, Shuheng Liu, Maximilian Ammenwerth et al.· 0 citations
Entanglement certification is often performed on states that have already undergone noisy transmission or processing. Noise can reduce the surviving entanglement and can also cause a given criterion to fail even when entanglement remains. In this context, the quantum switch, a paradigmatic realization of indefinite causal order (ICO), coherently controls the orders in which two channels act and has been shown to offer advantages across a range of quantum information-processing tasks. Here we ask whether this coherent control enlarges the noise-parameter region in which entanglement remains certifiable. We regard the two order branches as the arms of a causal-order interferometer and insert a local unitary between the channel uses to tune their interference. For stochastic Pauli noise, a postselected ICO output can exhibit greater entanglement negativity than any classical mixture of the two definite orders; in particular, we identify regimes where its negativity remains nonzero while that of every classical mixture vanishes. A suitable local Pauli unitary substantially enlarges this ICO-only region, while an input-dependent path-difference indicator qualitatively links operator noncommutativity to the postselected negativity gain. Numerical examples extend the advantage to local amplitude-damping noise and two-qutrit Weyl noise. At a representative Weyl-noise point for the $3\times 3$ positive-partial-transpose (PPT) Tiles bound-entangled state, a nondecomposable witness detects the postselected ICO output, whereas an analytic bound excludes detection of the definite-order outputs and their mixtures by the entire locally rotated witness family. These results identify causal-order interferometry as a strategy for enhancing entanglement certification across distinct noise models and dimensions.
Haojie Wang, Shuheng Liu, Qiongyi He· 0 citations
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