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arXiv:2512.13379

Fundamental error bound for entanglement generation between interacting Rydberg atoms

Georgios Doultsinos, Antonis Delakouras, David Petrosyan

quant-phSubmitted Dec 15, 2025• Announced Dec 16, 2025• 0 citations• Revised Aug 19, 2026 (v3)
v1 · Dec 15, 2025v2 · Dec 19, 2025v3 · Aug 19, 2026
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Abstract

We analytically derive the lower error bound for the preparation of any maximally entangled state of two atoms involving Rydberg-state interactions. This fundamental bound represents the minimum achievable error $E \geq ( 1 + π/2 ) Γ/B$ due to spontaneous decay $Γ$ of the Rydberg states and their finite interaction strength $B$, assuming that all other technical errors can be eliminated. Using quantum optimal control methods, we identify laser pulses for preparing a maximally entangled state of a pair of atomic qubits with an error only $1\%$ above the derived fundamental bound.

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9 pages, 2 figure

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We analytically derive the lower error bound for the preparation of any maximally entangled state of two atoms involving Rydberg-state interactions. This fundamental bound represents the minimum achievable error E≥(1+π/2)Γ/BE \geq ( 1 + π/2 ) Γ/BE≥(1+π/2)Γ/B due to spontaneous decay ΓΓΓ of the Rydberg states and their finite interaction strength BBB, assuming that all other technical errors can be eliminated. Using quantum optimal control methods, we identify laser pulses for preparing a maximally entangled state of a pair of atomic qubits with an error only 1%1\%1% above the derived fundamental bound.
We address a fundamental issue in quantum mechanics and quantum information theory---the generation of an entangled pair of qubits that interact solely through a third, semiclassical degree of freedom---in the framework of cavity quantum electrodynamics. We show that finite, although not maximal, entanglement is obtainable in the classical limit, at the price of a diverging effective interaction time. The optimal atomic entanglement derives from a trade-off between the atomic entanglement in a sub-wave packet and the purity of the atomic state. Decoherence by photon loss sets an upper limit on the degree of excitation of the cavity mode, beyond which the achievable entanglement decreases as the inverse mean photon number to the sixth power.
Generating entanglement between two Rydberg atoms is at the core of neutral-atom quantum computers. Current two-qubit gates operate in the Rydberg-blockade regime, in which the full strength of the van der Waals interaction between the two Rydberg atoms is not directly exploited, to avoid sensitivity to the position noise of the tweezer-trapped atoms, at the cost of a longer time spent in the Rydberg state. Here, we propose a set of techniques based on coherent control of the atomic motion obtained by combining optical tweezers and a two-dimensional optical lattice, and a sequence of multiple on/off pulses. The protocols keep the two-qubit gate error contribution from position noise below 10−410^{-4}10−4, heat the atom by less than~Δn=0.01Δn = 0.01Δn=0.01, while being robust to alignment errors of the potential up to 505050~nm and thermal excitation up to nˉ=3\bar{n} = 3nˉ=3. This toolbox opens the path for new two-qubit Rydberg gates directly, or partially, driven by the interaction, in which the atoms spend only ∼10\sim 10∼10~ns in the Rydberg state, minimizing the increasingly dominant error source originating from its finite lifetime.
Inspired by recent work [Carr and Saffman, Phys. Rev. Lett. 111, 033607 (2013)], we propose a simplified scheme to prepare the two-atom maximally entangled states via dissipative Rydberg pumping. Compared with the former scheme, the simplified one involves fewer classical laser fields and Rydberg interactions, and the asymmetric Rydberg interactions are avoided. Master equation simulations demonstrate that the fidelity and the Clauser-Horne-Shimony-Holt correlation of the maximally entangled state could reach up to 0.999 and 2.821, respectively, under certain conditions. Furthermore, we extend the physical thoughts to prepare the three-dimensional entangled state, and the numerical simulations show that, in theory, both the fidelity and the negativity of the desired entanglement could be very close to unity under certain conditions.
Abstract Quantum gates and entanglement based on dipole–dipole interactions of neutral Rydberg atoms are relevant to both fundamental physics and quantum information science. The precision and robustness of the Rydberg-mediated entanglement protocols are the key factors limiting their applicability in experiments and near-future industry. There are various methods for generating entangling gates by exploring the Rydberg interactions of neutral atoms, each equipped with its own strengths and weaknesses. The basics and tricks in these protocols are reviewed, with specific attention paid to the achievable fidelity and the robustness to the technical issues and detrimental innate factors.
We propose a scheme for rapid generation of high fidelity steady-state entanglement between a pair of atoms. A two-photon excitation process toward long-lived Rydberg states with finite pairwise interaction, a dark-state interference effect in the individual atoms, and spontaneous emission from their short-lived excited states lead to rapid, dissipative formation of an entangled steady state. We show that for a wide range of physical parameters, this entangled state is formed on a time scale given by the strengths of coherent Raman and Rabi fields applied to the atoms, while it is only weakly dependent on the Rydberg interaction strength.
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