⚛️ quantum physics

How To Track Qubits Through Space and Time (Or: Sailing in a Quantum Boat)

This paper introduces the concept of "quantum localization" to strengthen position-based cryptography by ensuring that unclonable quantum states or specific computational capabilities exist exclusively at a verified spacetime point, thereby enabling secure trajectory verification and addressing the limitations of existing location certification methods.

Original authors: James Bartusek, Zikuan Huang, Leo Orshansky, Henry Yuen

Published 2026-10-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: James Bartusek, Zikuan Huang, Leo Orshansky, Henry Yuen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to prove you are standing in a specific room without showing your face, your voice, or any ID card. In the world of cryptography, this is the goal of position-based security: using your physical location as your identity. For decades, scientists have tried to build systems where a person's presence at a certain spot is the only credential needed to unlock a door or sign a message. The challenge is that a group of tricksters could theoretically stand outside the room, copy messages, and pass them back and forth to fake being inside. Quantum mechanics, with its rule that you cannot perfectly copy unknown information, seemed to offer a solution. However, a gap remained in the logic: while quantum rules could stop a simple copy-and-paste attack, they did not guarantee that the same person was moving through the space over time. A team of stationary spies, each waiting at a different point along a path, could still fool the system by passing the baton of information between them, creating the illusion of a single traveler.

A team of researchers has now bridged this gap by introducing a new way to think about location that goes beyond simply checking a spot. They have developed a method to track a quantum object as it moves through space and time, ensuring that the information being verified is not just present, but is physically tied to a specific journey. Their work, published in a preprint, establishes a framework called "quantum localization." Instead of just asking, "Is someone here?" the new protocols ask, "Is the specific quantum state that started at point A still here at point B, and has it traveled the whole way?" This distinction is crucial because it prevents a distributed team of attackers from simulating a single traveler. The researchers proved that if a prover succeeds in their new tests, they must possess a unique, unclonable piece of information that exists only at that exact moment and place, making it impossible for the information to be split up or copied elsewhere.

The core of their achievement is a protocol that can verify a trajectory, or a path, through spacetime. In their setup, two fixed verifiers send out quantum challenges to a prover who claims to be moving along a specific line. The researchers designed a system using what they call a "quantum anchor." One part of this anchor stays safely with the verifiers, while the other part is sent to the prover. As the prover moves, they must interact with this traveling part in a way that proves they are carrying the original connection. If the prover attempts to bypass the system by having a team of people stand at different points along the line, the delicate quantum link breaks. The researchers showed that any successful prover must be able to "extract" the original quantum state at the verified location, proving that the information has physically traveled the path. This is a significant step forward because previous methods could only confirm that someone was at a location at a single moment, not that the same entity had moved continuously from one point to another.

To make this work, the team relied on a theoretical model involving "ideal obfuscation," which acts like a perfect, unbreakable black box for certain calculations. While this model is a mathematical ideal, the researchers argue that it can be approximated in the real world using advanced encryption techniques that are believed to be secure even against future quantum computers. They demonstrated that their protocols work in this setting, providing a rigorous proof that the localization of quantum information is possible. They also extended this idea to "functionality localization," which ensures that the ability to run a specific secret program is tied to a location. This means that even if someone has the code for a secret program, they cannot run it unless they are physically at the authorized spot, and they cannot copy the ability to run it to another location.

The paper also carefully addresses what this new method cannot do. The researchers explicitly showed that a well-known, simpler protocol called f-BB84, which was previously thought to be a strong candidate for position verification, fails their new, stricter test. In that older protocol, a group of attackers could successfully fake a single traveler by splitting the quantum information among three people, with the middle person doing the work while the others held the pieces of the puzzle. The new research proves that this kind of distributed strategy is exactly what their new protocols are designed to stop. By ruling out these distributed strategies, the work clarifies that true position verification requires more than just checking a box; it requires tracking the continuity of information.

This work lays a foundation for a future where digital trust is anchored in physical reality. By proving that quantum information can be tracked through space and time, the researchers have provided a stronger basis for secure communication that depends on location. Their findings suggest that we can move beyond the limitations of current systems, where a team of spies could mimic a single person, to a system where the physical journey of information is the only thing that matters. While the protocols currently rely on theoretical models that are difficult to build with today's technology, the mathematical proofs offer a clear path forward. The result is a deeper understanding of how location and information are linked, offering a new way to secure the digital world by tying it to the physical world.

Technical Summary: How To Track Qubits Through Space and Time

1. Problem Statement

Position-based cryptography (PBC) aims to use a party's physical location as their cryptographic credential. The standard primitive, Quantum Position Verification (QPV), involves verifiers sending quantum challenges to a prover at a claimed location $L$ and verifying responses arrive within strict timing constraints.

However, existing security definitions for QPV suffer from a conceptual gap. Current definitions only guarantee that at least one member of a distributed adversarial team is located at $L$ . This allows for "spoofing" scenarios where a team of adversaries, none of whom are at $L$ , jointly simulate a prover by distributing the necessary quantum information across space and time. Consequently, a successful QPV proof does not necessarily certify that a single, persistent entity was at the location, nor does it prevent a distributed team from simulating a moving prover.

This limitation prevents the realization of trajectory verification: the ability to verify that a prover has traveled along a specific path $L(\cdot)$ through spacetime. Running separate QPV protocols at different points along a trajectory fails to distinguish between a single moving prover and a chain of stationary provers, as the security guarantees of individual QPV protocols do not link the quantum state across time.

2. Methodology and Core Concepts

The authors introduce Quantum Localization, a stronger security notion that "pinpoints" the behavior of an adversary to a specific spacetime point $(L, t)$ by requiring the existence of a specific, unclonable object at that point. They define three types of localization:

Entanglement Localization: The ability to extract the verifier's half of an entangled pair from the prover's state at $(L, t)$ .
State Localization: The ability to extract a specific unclonable quantum state (e.g., from a family of coset states) from the prover at $(L, t)$ .
Functionality Localization: The ability to extract the capability to compute a secret function $f_k$ at $(L, t)$ , ensuring this capability cannot be computed elsewhere.

The Quantum Anchor State

The construction relies on a primitive called the Quantum Anchor State. This is a bipartite state $|\Psi\rangle_{\mathcal{A}\mathcal{V}}$ where:

$\mathcal{A}$ (Anchor) is held by the verifier.
$\mathcal{V}$ (Vessel) is sent to the prover.
The state is constructed from EPR pairs and "decoy" qubits, scrambled by a random change-of-basis unitary $U_{shift}$ .
The structure is defined by subspaces $S \le T \le \mathbb{F}_2^{3n}$ and shifts $u, v$ . The vessel register contains a superposition of coset states relative to these subspaces.

Non-Collapsing vs. Collapsing Oracles

A central technical innovation is the use of non-collapsing tests to verify entanglement without destroying it.

Collapsing Test: A standard measurement of the entangled state (e.g., in the standard or Hadamard basis) which collapses the wavefunction.
Non-Collapsing Test: The prover is given access to a classical oracle (modeled as ideal obfuscation) that checks membership in a subspace (e.g., $T+v$ or $S^\perp + u$ ) and returns a secret value if the query is valid. The prover performs a coherent query to this oracle.
Indistinguishability: Using the Compressed Oracle technique and subspace indistinguishability lemmas, the authors prove that a prover passing the non-collapsing test (which does not collapse the state) is indistinguishable from a prover who would pass the corresponding collapsing test. This allows the verifier to extract the entanglement or state after the protocol, even though the protocol itself did not destroy the state.

Monogamy-of-Entanglement Games

To prove security, the authors define Multi-Stage Monogamy-of-Entanglement Games. These games model an adversary (split into Left, Middle, and Right components) attempting to answer challenges at different spacetime points.

The security proof relies on showing that if an adversary succeeds with high probability, the "Middle" component (at the verified location) must have performed a measurement (or oracle query) that effectively collapsed the state locally.
By leveraging the Monogamy of Entanglement, they show that the adversary cannot maintain correlations with the verifier's anchor at multiple locations simultaneously. If the adversary succeeds, the entanglement must have been localized to the specific spacetime point where the query occurred.

3. Key Contributions and Results

1. Entanglement Localization

The paper constructs a protocol where the verifier can extract the entangled partner of their anchor state from the prover's state at a specific spacetime point $(L, t)$ .

Result: If a prover strategy is accepted with non-negligible probability, there exists an extractor that, given the state at $(L, t)$ , outputs a register with high fidelity to the original entangled state.
Regime: The protocol is secure in the Ideal Obfuscation Model (classical oracle model), which can be heuristically instantiated using post-quantum indistinguishability obfuscation (iO) and one-way functions.

2. Trajectory Verification

Building on entanglement localization, the authors define Trajectory Verification.

Mechanism: The verifier sends the "vessel" register to the prover and runs a sequence of entanglement localization protocols at discrete points $(L(t_i), t_i)$ along the claimed trajectory.
Result: If the prover is accepted, the entanglement is localized to every point on the trajectory. By the Monogamy of Entanglement, this implies a single quantum system (the vessel) traveled along the path $L(\cdot)$ . This rules out the "chain of stationary provers" attack, as such a chain cannot maintain the required entanglement across the entire trajectory simultaneously.

3. State and Functionality Localization

State Localization: The authors show that the techniques can be adapted to localize specific quantum states (e.g., BB84 states or coset states) rather than just entanglement. The extractor recovers the specific state $|\psi_k\rangle$ at the verified location.
Functionality Localization: They introduce a notion where the prover must possess the ability to compute a secret function $f_k$ at the verified location. This is achieved by combining localization techniques with Quantum State Obfuscation (best-possible copy protection). The result guarantees that the computational capability is localized to $(L, t)$ and cannot be computed elsewhere.

4. Negative Result: Non-Localizability of $f$ -BB84

The paper demonstrates that not all QPV protocols satisfy localization. They show that the well-studied $f$ -BB84 protocol (where a prover measures an EPR pair based on a function $f(x,y)$ ) is not entanglement-localizable.

Attack: A distributed team of three provers can simulate the protocol perfectly by sharing a quantum one-time pad. The middle prover performs the correct measurement, but the entanglement is distributed non-locally among the three provers, preventing any single extractor from recovering the full entangled state at the middle location. This highlights the strength of the new localization definitions.

4. Significance and Claims

The authors claim that their work provides a stronger foundation for position-based cryptography by addressing the gap between intuitive goals (tracking a physical entity) and formal security definitions.

Conceptual Shift: The paper moves PBC from a binary "is someone there?" verification to a continuous "is this specific quantum information here?" verification.
Trajectory Verification: It provides the first feasibility result for verifying the trajectory of an entity through spacetime, a task previously considered ill-defined or impossible under standard QPV security.
Physical Spacetime and Information: The results explore the tight link between location and information, suggesting that cryptographic capabilities can be fundamentally tied to physical spacetime constraints via quantum mechanics.
Model: The security is proven in the Ideal Obfuscation Model. The authors acknowledge this is a heuristic assumption (instantiated via iO) but argue it is a standard and necessary step for such strong primitives, similar to the use of the Random Oracle Model in classical cryptography. They explicitly state that proving security in the plain model (without oracles) remains a major open problem.

The paper concludes by noting that while their protocols currently assume noiseless transmission and precise timing, the framework offers a theoretical basis for future robust, real-world implementations of location-based quantum credentials.