Port-based teleportation under pure-dephasing decoherence

TL;DR

This work analyzes deterministic port-based teleportation under pure-dephasing decoherence that acts on each entangled link, considering both resource-only noise with ideal measurements and noise-adapted measurements. It derives a closed-form entanglement-fidelity expression for the resource-noise case and a semi-analytic approach for the optimized-measurement scenario, finding that noise-adapted measurements can underperform the noiseless protocol. By embedding the protocol in a spin–boson model, the authors connect the teleportation fidelity to microscopic bath properties, showing that temperature and bath memory critically influence performance and that non-Markovian effects yield nontrivial short-time dynamics. The results provide analytical bounds, exact expressions in key limits, and numerical insights that clarify PBT robustness to realistic noise and guide future optimization under correlated environments and broader noise models.

Abstract

We study deterministic port based teleportation in the presence of noise affecting both the entangled resource state and the measurement process. We focus on a physically motivated model in which each Bell pair constituting the resource interacts with an identical local environment, corresponding to independently distributed entangled links. Two noisy scenarios are analyzed: one with decoherence acting solely on the resource state and ideal measurements, and another with noisy, noise adapted measurements optimised for the given noise model. In the first case, we derive an analytical lower bound and later a closed-form expression for the entanglement fidelity of the teleportation channel and analyze its asymptotic behaviour. In the second, we combine semi analytical and numerical methods. Surprisingly, we find that noise-adapted measurements perform worse than the noiseless ones. To connect the abstract noise description with microscopic physics, we embed the protocol in a spin boson model and investigate the influence of bath memory and temperature on the teleportation fidelity, highlighting qualitative differences between different environments.

Figures (5)

• Figure 1: The average teleportation fidelity for $N=9$, calculated using the entanglement fidelity Eq. \ref{['ent_fid_NL']}, is plotted against $|\Gamma|$ and $\theta$. The results are shown as (a) a three-dimensional surface plot and (b) a contour plot.
• Figure 2: Teleportation fidelity $f=(2F+1)/3$ as a function of $N$ for four various choices of the noise parameters $(|\Gamma|,\theta)$. The blue line reproduces the noiseless case from the Hiroshima-Ishizaka protocol.
• Figure 3: (a) The average teleportation fidelities for noiseless Ishizaka-Hiroshima POVMs (solid lines) computed using Eq. \ref{['ent_fid_NL']} and the average teleportation fidelities for PGM (dhashed lines) computed using eigensolver python program are plotted for $N=2,5,9$. The Beigi-König bound for $N=9$ is plotted with blue dashed-dotted line. (b) Average teleporation fidelities for noiseless POVMs (blue solid), PGM (orange dashed-dotted) and the maximum fidelity as per Helstrom bound (green dashed) are plotted for $N=2$.
• Figure 4: Average teleportation fidelity $f(\tau)$ for $N=9$ as a function of the dimensionless time $\tau=t\Lambda$ for a generalized Ohmic bath with Ohmicity $s=2$ ($s=3$) and transit time $\ell=\Lambda\bar{t}=3$. Solid lines -- noiseless measurements; dashed lines -- noise-adapted measurements. Each curve corresponds to a fixed temperature ratio $T/\Lambda=0.1$ or $T/\Lambda=0.9$.
• Figure 5: The correction term $F_{corr}$ from expression \ref{['eq:S-final']}. We see non-monotonicity behaviour for small value of $N$. The function $F_{corr}$ achieves maximum value $F_{corr}\approx 0.2327$ for $N=6$. For $N >6$ the correction term vanishes monotonically, achieving 0 for $N\rightarrow \infty$.

Theorems & Definitions (2)

• Lemma 1
• proof