Quantum Ranging Enhanced TDoA Localization

TL;DR

This work addresses the limitations of classical TDoA localization by introducing quantum-enhanced ranging that uses entangled probe states to encode a signed sum of distances, $\sum_{i\in I_k} \omega_{i,k} \|\mathbf{x}-\mathbf{a}_i\|$, into a single measurement extractable via phase estimation. Localization is formulated as a non-convex problem and then relaxed to a convex conic program using auxiliary variables and lifted matrices, solvable as a SDP/SOCP with interior-point methods; a CRLB analysis provides theoretical performance bounds. Numerical results in 3D show substantial improvements over classical TDoA, with average gains exceeding 50% and performance tracking the CRLB under increasing noise, validating the proposed quantum-enhanced paradigm. The work highlights a practical pathway to reduce ranging errors in TDoA systems and motivates future exploration of measurement design, anchor geometry, and more efficient solvers for quantum-assisted localization.

Abstract

Localization is critical to numerous applications. The performance of classical localization protocols is limited by the specific form of distance information and suffer from considerable ranging errors. This paper foresees a new opportunity by utilizing the exceptional property of entangled quantum states to measure a linear combination of target-anchor distances. Specifically, we consider localization with quantum-based TDoA measurements. Classical TDoA ranging takes the difference of two separate measurements. Instead, quantum ranging allows TDoA estimation within a single measurement, thereby reducing the ranging errors. Numerical simulations demonstrate that the new quantum-based localization significantly outperforms conventional algorithms based on classical ranging, with over 50% gains on average.

Figures (1)

• Figure 1: ME under various settings with respect to noise