Curator's Take
This article introduces quantitative “absorption capacities” that tell exactly how much Bell‑state weight a separable two‑qubit noise can tolerate before it becomes entangled or useful for teleportation, giving hardware engineers clear thresholds for when their devices cross from classical to quantum performance. By deriving closed‑form formulas for product and X‑type noise—and showing how these capacities evolve under realistic amplitude‑damping and dephasing channels—it links abstract separability criteria directly to the practical noise budgets of near‑term processors. The results complement recent studies on entanglement robustness, offering a handy tool for benchmarking and improving error mitigation strategies in quantum hardware.
— Mark Eatherly
Summary
We study Bell-mixing lines $ρ_λ=λΦ^+ +(1-λ)σ$, where $Φ^+$ is a fixed Bell reference and $σ$ is a separable two-qubit noise state. Along this line there are two operational crossings: the state becomes entangled, and it reaches quantum teleportation advantage over classical strategies. We package these crossings as capacities of the noise state. The entanglement absorption capacity $C_{\rm abs}(σ)$ is the largest amount of Bell reference that $σ$ can absorb while the partial transpose remains positive. The fidelity absorption capacity $C_F(σ)$ is the largest amount of Bell reference that $σ$ can absorb while keeping the maximal teleportation fidelity at or below the classical bound $2/3$. The thresholds corresponding to the two crossing points are obtained from the same Möbius map, $λ_* = C_{\rm abs}/(1+C_{\rm abs})$ and $λ_F = C_F/(1+C_F)$. We derive closed-form capacities and thresholds for product noise states and separable complex $X$ noise states. For product noise, $C_{\rm abs}$ depends only on local marginal purities, while $C_F$ also depends on orientation relative to the maximally entangled reference. For $X$ noise states, both capacities are explicit in all four Bell frames. We also study three extensions: arbitrary pure-state references, the evolution of $X$ noise states and their capacities under local amplitude-damping and dephasing channels, and decomposition certificates that give lower bounds on the capacities, hence on the thresholds, for general separable noise.