Relativistic Position Verification with Coherent States

Abstract

Determining the position of an entity is a fundamental prerequisite for nearly all activities. Classical means, however, have been proven incapable of providing secure position verification, meaning that a prover can mislead verifiers about its actual position. In this work, we propose and experimentally realize a secure position-verification protocol that leverages quantum optics and relativity within an information-theoretic framework. Using phase-randomized weak coherent states, two verifiers separated by 2 km securely verify the prover's position with an accuracy better than 75 meters. These results establish secure position-based authentication as a practical possibility, paving the way for applications in financial transactions, disaster response, and authenticated secure communications.

Figures (2)

• Figure 1: Quantum position verification protocol using coherent states. The position of the prover, $P$, is verified by two spatially separated verifiers, $V_1$ and $V_2$. a. Information flow in a single round of position verification. $V_1$ and $V_2$ each send $n/2$ classical bits to $P$. Simultaneously, $V_1$ sends a coherent state $\ket{\alpha_{b,c}}$ with mean photon number $\abs{\alpha}^2$, whose polarization is determined by eigenbasis $b$ and eigenvalue $c$. $P$ evaluates the Boolean function $f:\{0,1\}^n\to b$ to obtain $b$, measures ($\mathcal{M}$) the polarization of the quantum state accordingly, and returns the result $c'$ as a credential to the verifiers for verification. b. Light-cone interpretation of position precision. Without any delay, $P$ is precisely located at the intersection of the light cones from $V_1$ and $V_2$. An excess delay $\Delta t$ allows all events within a range $\Delta r$ to satisfy the verification condition, so $P$'s position is constrained within $\Delta r$.
• Figure 2: Experimental setup for quantum position verification. From left to right are $V_1$, $P$, and $V_2$, spaced approximately 0.98 km apart in sequence. The classical bits preparation unit (CPU) and quantum state preparation unit (QPU) of the verifiers implement the Message Preparation step of the protocol, while the credential receive unit (CRU) implements the Position Inference step. The prover's Boolean function unit (BFU) and quantum state measurement unit (QMU) implement the Credential Generation step. The quantum states are prepared in the $\ket{H}+e^{i\phi}\ket{V}$ polarizations using a Sagnac interferometer including a phase modulator (PM) and a micro-assembled rotated circulating splitter (RCS), and transmitted to $P$ through ultra-low-loss fiber (ULL-F). All classical signals are sent using a laser array in dense-wavelength-division-multiplexed on–off keying (DWDM-OOK) and received by high-speed PIN detectors, transmitted near the speed of light through anti-resonant hollow-core fiber (AR-HCF). The BFU is implemented using table lookups and logic computations on an FPGA with 1-Tb DDR memory, where the PIN array signals serve as addresses and the stored data as the output measurement basis. The QMU uses high-voltage driven a low-loss optical switch (OS) to select a measurement basis and superconducting detectors (DET) for detection. $V_1$ and $V_2$ employ time-to-digital converters (TDCs) to capture the returned measurement signals and record the latency. ATT, attenuator; PC, polorization controller; BS, beam splitter; PBS, polarizing beam splitter.