Quantum Position Verification with Remote Untrusted Devices

TL;DR

This work addresses secure localization of remote parties by implementing a device-independent quantum position verification protocol that relies on loophole-free Bell tests across a quantum network. The authors develop a spacetime-circuit security framework, reduce adversarial strategies to three-party non-signaling models, and construct test factors that certify prover presence in a target spacetime region while tolerating limited prior entanglement. Experimentally, they realize the protocol with two verifiers separated by 195.1 m and a prover located 92.8 m from one verifier, achieving a quantum localization region smaller than any equivalent classical target region by factors up to $4.53\pm0.05$ in 3D (and $2.47\pm0.02$ in 1D against an ideal classical protocol), at rates around $2.5\times 10^5$ trials per second and detection efficiencies >$81\%$. The results demonstrate a robust, device-independent cryptographic primitive that anchors digital security to physical geography, with potential implications for secure network authentication, location-based cryptography, and quantum communications.

Abstract

Many applications require or benefit from being able to securely localize remote parties. In classical physics, adversaries can in principle have complete knowledge of such a party's devices, and secure localization is fundamentally impossible. This limitation can be overcome with quantum technologies, but proposals to date require trusting vulnerable hardware. Here we develop and experimentally demonstrate a protocol for device-independent quantum position verification that guarantees security with only observed correlations from a loophole-free Bell test across a quantum network. The protocol certifies the position of a remote party against adversaries who, before each instance of the test, are weakly entangled, but otherwise have unlimited quantum computation and communication capabilities. Our demonstration achieves a one-dimensional localization that is 2.47(2) times smaller than the best, necessarily non-remote, classical localization protocol. Compared to such a classical protocol having identical latencies, the localization is 4.53(5) times smaller. This work anchors digital security in the physical world.

Figures (16)

• Figure 1: Schematic representations of position verification protocols and possible attacks. Subfigure A shows an (insecure) classical protocol for position verification that tries to enforce the target region in yellow with classical challenges from the verifiers ${\sf A}$ and ${\sf B}$. The verifiers desire that the computation $g(u_{{\sf A}}, u_{{\sf B}})$ is localized to the target region. Subfigure B sketches a specific attack on the classical protocol, with adversaries $\mathcal{A}_{{\sf A}}$ and $\mathcal{A}_{{\sf B}}$, situated in the blue regions outside the target regions, each performing the computation locally. By communicating the challenge bits to one another, they can spoof a successful pass of the classical protocol. To ensure security against general attacks perpetrated by unentangled or weakly entangled adversaries, we introduce our quantum protocol, sketched in subfigure C. Here, the honest prover ${\sf P}$ and a quantum measurement station ${\sf A}'$ located at ${\sf A}$ share an entangled state $|\Phi\rangle$. The state is measured using untrusted quantum hardware, with the measurement basis at ${\sf A}$ decided by a local random number generator and the basis at ${\sf P}$ decided by the output of $f(u_{{\sf A}}, u_{{\sf B}})$. Subfigure D is a schematic of the spatial extents of the target regions enforceable by the classical (blue and yellow) and quantum (yellow) protocols, projected into two-dimensions for the specific case of a realistic two-verifier protocol.
• Figure 2: Figure depicting the spacetime target regions in our protocol. Subfigure A depicts a two-dimensional spacetime slice, where the spatial dimension is along the line joining the provers, here assigned the $x$-axis. Both the quantum (yellow), and comparable classical (blue) regions are completely defined by forward and backward lightcones from the spacetime events corresponding to the release of $u_{{\sf A}}{}$ and $u_{{\sf B}}{}$ and the last moments when $z_{{\sf A}}{}$ and $z_{{\sf B}}{}$ are accepted. Events $o_{{\sf A}'}{}$ and $m_{{\sf A}'}$ occur at ${\sf A}'$, which is slightly displaced from ${\sf A}$. Subfigures B and C show three-dimensional projections of the quantum and classical target regions, with the time dimension vertically up on the page, and the spatial dimensions parallel and perpendicular to the verifier axis depicted in the other two directions. The regions are all rotationally symmetric about the verifier axis, and so are identical in the spatial dimensions ($y$ and $z$) perpendicular to the verifier axis.
• Figure 3: Figure depicting the experimental setup and verifier and prover stations used for our demonstration. Subfigure A depicts the quantum target region $E$ of our protocol in yellow, and the classical target region of a comparable classical protocol in blue overlaid on an aerial photograph of the NIST building, where the experiment is housed. Subfigure B shows a schematic of the hardware at verifier ${\sf A}$. From an entangled photon pair source, one photon of the pair is sent to prover ${\sf P}$, and the other to the measurement station ${\sf A}'$. At measurement station ${\sf A}'$, the incoming photon is delayed in a fiber loop and measured by a superconducting nanowire detector in a polarization basis determined by a fast Pockels cell and waveplates. The setting is chosen via a random number generator (RNG), and the outcome is recorded on a time-tagger. Subfigure C depicts the measurement station at the prover ${\sf P}$. The choice of measurement basis here is set via an XOR of the bits $u_{{\sf A}}$ and $u_{{\sf B}}$ from the verifiers. The outcome of this measurement is sent back to both verifiers, who record it on their timetaggers. SNSPD: Superconducting nanowire single photon detector; XOR: Exclusive OR; PC: Pockels cell; HWP: Half-wave plate; QWP: Quarter-wave plate.
• Figure 4: Plots of results from our experimental runs. Two sets of protocol instances were run as part of our demonstration: subfigure A is day 1, analyzed for security against adversaries pre-sharing no entanglement; and subfigure B is day 2, analyzed against adversaries pre-sharing entanglement such that the average robustness over an instance's trials is upper bounded by $r_{\text{th}} = 8\times 10^{-6}$. The soundness target for all instances was $\delta = 2^{-64}$. Plotted are histograms of the data binned based on their calculated $\log_2(P)$ value. The $\log_2(P)$ value of each protocol instance is indicated with a tick directly above the $x$-axis and below the histograms on both plots. Any instances with a $\log_2(P)$ less than $-\log_2(\delta) = 64$ are declared failures, and correspond to ticks inside the red regions. Also plotted in purple is the experimental fraction of instances below $\log_2(P)$ as a function of $\log_2(P)$. At a higher $\log_2(P)$, which corresponds to a stricter choice for the soundness, a larger fraction of the data would be considered a failure, reducing success probability. The plots both share the same $x$-axis.
• Figure 5: Experimental diagram for the position verification demonstration. Verifiers ${\sf A}$, ${\sf A}'$, and ${\sf B}$, the honest prover ${\sf P}$ as implemented, and the entangled photon source ${\sf A_{\text{source}}}$ are indicated. The yellow shading around the honest prover indicates the region prover hardware must be in to pass the protocol (target region $E$). The RNGs and timetaggers are associated with the verifiers. Electrical and optical cables carry information to and from the various experimental stations. The entangled photons are distributed via optical cables, and the measurement choice bits are transmitted via high-speed coaxial cables. Electrical cables are indicated in black, and optical cables in orange. Electrical-to-optical (OE) and optical-to-electrical (EO) converters convert information between electrical and optical encoding. These are used in the lines that transmit synchronization signals among the verifiers. ${\sf A_{\text{source}}}$ is the source of entangled photons, which produces entangled photons via spontaneous parametric downconversion with a periodically poled potassium titanyl phosphate (ppKTP) crystal placed inside a dual Mach-Zehnder interferometer formed with beam displacers (BD) kavuri_traceable_2025. For the measurements at ${\sf A}'$ and ${\sf P}$, the pair of measurement bases are implemented with quarter-waveplates (QWP) and half-waveplates (HWP), and fast switching between the bases is performed with a Pockels cell.