Resource-Efficient Teleportation of High-Dimensional Quantum Coherence via Initial Phase Engineering

TL;DR

This work presents REHDCT, a resource-efficient protocol for teleporting quantum coherence in high-dimensional systems by replacing $d^2$ Bell-state measurements with $d$-outcome POVMs, cutting measurement complexity from $O(d^2)$ to $O(d)$ and halving classical communication to $\log_2 d$. Central to the scheme is initial phase engineering, which aligns the target qudit's phase with the POVM basis to achieve theoretically perfect coherence teleportation for arbitrary states, with robustness to phase deviations demonstrated experimentally-like in simulations (e.g., $\eta>0.996$ for $d=16$ at $\delta_\phi=0.1$ rad). The authors develop a CJKS-based noise framework to analyze the protocol under AD, PF, DP, and DF channels, deriving noise thresholds and showing that the quantum advantage window expands with dimension; notably, a perfect measurement basis can render DF noise inconsequential for $x=0$. The results suggest REHDCT as a practical framework for resource-constrained high-dimensional quantum networks, enabling efficient coherence transfer with hardware-friendly measurement schemes and phase-matching strategies that bolster resilience against realistic noise.

Abstract

High-dimensional quantum systems leverage an expanded Hilbert space to enhance resilience against decoherence and noise. However, standard quantum teleportation is fundamentally limited by the quadratic growth of measurement complexity and high classical communication overhead, requiring the resolution of $d^2$ Bell states and $2\log_2 d$ classical bits. In this study, we propose a resource-efficient high-dimensional coherence teleportation (REHDCT) protocol. By designing $d$ sets of specialized positive operator-valued measure (POVM) bases, our protocol achieves a 50\% reduction in classical communication by utilizing one of the $d$ designed POVM sets, which effectively scales the measurement complexity from $O(d^2)$ to $O(d)$. Furthermore, we demonstrate that by utilizing initial phase engineering to align the target qudit with the measurement basis, theoretically perfect teleportation of quantum coherence can be achieved for arbitrary qudit states. A quantitative robustness analysis reveals that the protocol remains highly resilient to operational errors, maintaining an efficiency above 99.6\% even under a 0.1 rad phase deviation for $d=16$. Our analysis under various noise models (amplitude damping, phase flip, depolarizing, and dit-flip) confirms that high-dimensional systems exhibit an expanding quantum advantage window as dimensionality increases. Notably, under dit-flip noise, perfect coherence teleportation can be restored through the optimal selection of the POVM basis. These findings establish REHDCT as a practical, hardware-friendly framework for resource-efficient quantum communication in future high-dimensional networks.

Figures (4)

• Figure 1: (Color online) Schematic representation of the REHDCT protocol under environmental noise. The target qudit $T$ undergoes initial phase engineering to ensure the phase-alignment condition (\ref{['phase']}) is satisfied prior to the protocol. The shared maximally entangled state $\rho_{AB}$ is subjected to local noise channels $\mathcal{E}_{A}$ and $\mathcal{E}_{B}$. Alice performs a resource-efficient measurement utilizing the POVM set $\{\Pi_x\}$, which effectively scales the measurement complexity down to $O(d)$.
• Figure 2: (Color online) The efficiency of QC teleportation for qudits of varying dimensions under AD noise. The horizontal lines corresponds to the classical bounds. The red dots indicate the positions of $p_{\rm AD}^{\rm th}$. The inset: The noise threshold $p_{\rm AD}^{\rm th}$ as a function of dimensionality $d$.
• Figure 3: (Color online) The efficiency of QC teleportation for qudits of varying dimensions under PF noise. The horizontal lines corresponds to classical bounds. The red dots indicate the positions of $p_{\rm PF}^{\rm th}$. The inset: The noise threshold $p_{\rm PF}^{\rm th}$ as a function of dimensionality $d$.
• Figure 4: The efficiency of QC teleportation for qudits of varying dimensions under DP noise. The horizontal lines corresponds to classical bounds. The red dots indicate the positions of $p_{\rm DP}^{\rm th}$. The inset: The noise threshold $p_{\rm DP}^{\rm th}$ as a function of dimensionality $d$.