Quantifying electron-nuclear spin entanglement dynamics in central-spin systems using one-tangles

Optically-active solid-state systems such as self-assembled quantum dots, rare-earth ions, and color centers in diamond and SiC are promising candidates for quantum network, computing, and sensing applications. Although the nuclei in these systems naturally lead to electron spin decoherence, they can be repurposed, if they are controllable, as long-lived quantum memories. Prior work showed that a metric known as the one-tangling power can be used to quantify the entanglement dynamics of sparse systems of spin-1/2 nuclei coupled to color centers in diamond and SiC. Here, we generalize these findings to a wide range of electron-nuclear central-spin systems, including those with spin > 1/2 nuclei, such as in III-V quantum dots (QDs), rare-earth ions, and some color centers. Focusing on the example of an (In)GaAs QD, we offer a procedure for pinpointing physically realistic parameter regimes that yield maximal entanglement between the central electron and surrounding nuclei. We further harness knowledge of naturally-occurring degeneracies and the tunability of the system to generate maximal entanglement between target subsets of spins when the QD electron is subject to dynamical decoupling. We also leverage the one-tangling power as an exact and immediate method for computing QD electron spin dephasing times with and without the application of spin echo sequences, and use our analysis to identify coherence-sustaining conditions within the system.

💡 Research Summary

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The manuscript presents a comprehensive theoretical framework that extends the concept of one‑tangling power—a metric originally devised for central‑spin systems with spin‑½ nuclei—to encompass arbitrary nuclear spin magnitudes. The authors begin by recalling that the one‑tangle, defined as the linear entropy (τ = 1 − Tr ρ²) of a bipartition, quantifies the entanglement of a pure state across that cut. By averaging the one‑tangle over all possible product initial states, they obtain the one‑tangling power ε, which measures the intrinsic ability of a unitary evolution U to generate entanglement irrespective of the system’s preparation.

In earlier works, ε was linked linearly to the first Makhlin invariant G₁ for block‑diagonal unitaries of the form U = |0⟩⟨0|⊗R₀ + |1⟩⟨1|⊗R₁, but this relation held only for spin‑½ nuclei (dimension d = 2). The present paper generalizes the derivation by allowing each nuclear subsystem i to have dimension d_i = 2I_i + 1, where I_i is the nuclear spin. The resulting expressions are:

• For a single isolated nucleus i: \