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arxiv: 2605.30732 · v1 · pith:Y3WYVUOXnew · submitted 2026-05-29 · 🪐 quant-ph · cs.CR

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

James Bartusek , Zikuan Huang , Leo Orshansky , Henry Yuen This is my paper

Pith reviewed 2026-06-28 22:21 UTC · model grok-4.3

classification 🪐 quant-ph cs.CR
keywords quantum localizationposition verificationtrajectory verificationunclonable statesposition-based cryptographyquantum anchor statesfunctionality localization
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The pith

Quantum localization requires a unique unclonable state at one spacetime point and nowhere else.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper strengthens position verification in quantum cryptography by introducing quantum localization. This requires that a specified unclonable quantum state is present at the claimed spacetime location and cannot be found anywhere else. Such localization naturally enables trajectory verification, allowing quantum information to be tracked verifiably through space and time. The authors also define functionality localization for secret computations tied to specific points in spacetime. These ideas use quantum anchor states and aim to give stronger foundations for position-based cryptography.

Core claim

Using quantum anchor states that generalize coset states, the authors construct protocols for quantum localization where a specified unclonable state must be at the verified spacetime point and nowhere else, and for trajectory verification to track such states through space and time. Security holds in the classical oracle model.

What carries the argument

Quantum anchor states, generalizing coset states from unclonable cryptography, to enforce the presence of a unique state at a spacetime point.

If this is right

  • Distributed adversaries cannot jointly simulate the prover without the state being at the location.
  • Quantum information can be verifiably tracked along a trajectory in space and time.
  • Computational capabilities can be localized so a secret function is computable only at the verified point.
  • Position-based cryptography receives stronger security definitions against cloning attacks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • These notions could support applications in quantum networks where location and state uniqueness are critical.
  • Testing the protocols under physical noise might reveal practical limitations of the unclonability.
  • Functionality localization raises questions about tying computations to physical locations in quantum systems.

Load-bearing premise

Security depends on the classical oracle model for obfuscation, which is heuristically realized using post-quantum indistinguishability obfuscation.

What would settle it

An explicit attack allowing an adversary to have the required unclonable state at more than one location would disprove the localization property.

Figures

Figures reproduced from arXiv: 2605.30732 by Henry Yuen, James Bartusek, Leo Orshansky, Zikuan Huang.

Figure 1
Figure 1. Figure 1: A quantum anchor. Generated by GPT. 1.2 State Localization A curious aspect of the entanglement localization and trajectory verification protocols described above is that the verifier’s register (the quantum anchor) is never acted upon after the entangled state is prepared. In fact, the verifiers don’t even need this register to check the prover’s responses. Thus, a slightly different way to describe the g… view at source ↗
Figure 2
Figure 2. Figure 2: Non-localizability attack on 𝑓-BB84 Consider the following 3 prover strategy, pictured in [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: shows the non-collapsing test when 𝑈𝗌𝗁𝗂𝖿𝗍 = 𝐼 and 𝜃 = 0. Only the correctness of the standard-basis qubits is tested. One may notice that this is a non-collapsing test, and the state is unchanged after the test is completed. 𝐀: 𝐁: + − ... + + Hadamard-basis Qubits ... ... 0 1 ... 1 0 Standard-basis Qubits ✓ ✓ ✓ ✓ [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The Collapsing Test. In the collapsing test, each potential measurement result 𝑥 obtained by the verifier corresponds to a different input on which the honest prover queried 𝒪𝗋𝖺𝗇𝖽𝗈𝗆. In the main proof, we show that any (potentially adversarial) prover that passes with probability close to 1 in the non-collapsing test will yield the following behavior in the collapsing test with overwhelming probability: • … view at source ↗
Figure 5
Figure 5. Figure 5: Compact state-generation diagram. 𝖦𝖾𝗇𝖠𝗇𝖼𝗁𝗈𝗋𝖲𝗍𝖺𝗍𝖾 and 𝖣𝗈𝗆𝖺𝗂𝗇𝖤𝗑𝗍𝖾𝗇𝗌𝗂𝗈𝗇. 𝖦𝖾𝗇𝖠𝗇𝖼𝗁𝗈𝗋𝖲𝗍𝖺𝗍𝖾 and 𝖣𝗈𝗆𝖺𝗂𝗇𝖤𝗑𝗍𝖾𝗇𝗌𝗂𝗈𝗇 are shown in [PITH_FULL_IMAGE:figures/full_fig_p027_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The multi-stage monogamy-of-entanglement game MultiStageSearch￾Monogamy/MultiStageDecisionMonogamy. The main result of this section is Lemma 6.20. Intuitively, it states that any adversary passing the above game with good probability has to recover the value of 𝑏0 by querying its oracle already at the time BeforeSplit. Formally, we show that for each value of 𝑏0, the states corresponding to 𝑏0 at BeforeSpl… view at source ↗
Figure 7
Figure 7. Figure 7: The modified multi-stage decision monogamy-of-entanglement game ModifiedMultiStageDecision￾Monogamy. probability between ModifiedMultiStageDecisionMonogamy and MultiStageDecisionMonogamy. In the game ModifiedMultiStageDecisionMonogamy, the state at BeforeSplit is ∝ ∑︁ 𝗌𝗄 ∑︁ 𝑥 ∑︁ 𝑏 ′ ,𝑏∈𝔽2 𝛼𝗌𝗄,𝑥 |𝗌𝗄⟩ø |𝑥⟩ ⃒ ⃒𝑏 ′ 0 ⟩︀ 𝐁′ |𝑏0⟩𝐁 ⃒ ⃒ ⃒𝜓 𝗌𝗄 𝑥,𝑏′ 0 ⟩ 𝐋𝐌𝐑 . In the game MultiStageDecisionMonogamy, the state at Befo… view at source ↗
Figure 8
Figure 8. Figure 8: The adversary ℬ = (ℬ𝑀, ℬ𝐿, ℬ𝑅). 1. The challenger generates (︁ 𝗌𝗄, ⃒ ⃒Ψ𝗌𝗄 𝑛𝑒,𝑛,𝑛⟩︀ ê )︁ ← 𝖦𝖾𝗇𝖠𝗇𝖼𝗁𝗈𝗋𝖲𝗍𝖺𝗍𝖾𝑛𝑒,𝑛,𝑛(1𝜆 ) and gives the reg￾ister ê to ℬ𝑀. It samples uniformly random subspace 𝑇 * of dimension 𝑛𝑒 + 7𝑛/4 such that 𝑇 ≤ 𝑇 * ≤ 𝔽 𝑛𝑒+2𝑛 2 . It also samples uniformly random subspace 𝑆 * ≤ 𝑆 of dimension 𝑛/4. 2. ℬ𝑀 is given membership oracles 𝒪𝑇 *+𝑣 and 𝒪𝑆*⊥+𝑢 . ℬ𝑀 can choose to abort in this step. If it… view at source ↗
Figure 9
Figure 9. Figure 9: The dual multi-stage monogamy-of-entanglement game DualMultiStageSearchMonogamy. for inverse polynomials 𝜀(𝜆), 𝜀′ (𝜆). Then running ℰ 𝒜1 𝑀 𝐻 on the state 𝐌 conditioned on 𝒜0 𝑀 not aborting gives 𝑥, the Hadamard basis measurement result on , with probability at least 1 − 2 √ 2𝜀 1/2 − 𝗇𝖾𝗀𝗅(𝜆). That is, with 𝐗 denoting the output register of ℰ 𝒜1 𝑀 𝐻 , 𝔼 [︂ 𝖳𝗋 (︂ Π𝖾𝗊ℰ 𝒜1 𝑀 𝐻 𝜌𝐗𝐌 (︁ ℰ 𝒜1 𝑀 𝐻 )︁† Π𝖾𝗊)︂⃒ ⃒ ⃒ ⃒ (… view at source ↗
Figure 10
Figure 10. Figure 10: Spacetime decomposition of the prover 𝒜 for our localization reduction, shown with 𝐿 = 0. Claim 8.5. For any prover 𝒫 * that passes with probability 1−𝜂, the probability that 𝒜 wins Definition 7.8 is at least 1 − 𝜂 − 𝗇𝖾𝗀𝗅. Proof. By [Zha12, Theorem 3.1], the 2𝑟-wise independent hash function perfectly simulates the random oracle for 𝒫 * . Also we can see that 𝒜 perfectly simulates 𝒫 * , since for any even… view at source ↗
Figure 11
Figure 11. Figure 11: Spacetime decomposition of the reduction 𝒜 for trajectory verification, where the prover is moving between checkpoints. In this picture, 𝐿 = 0 and 𝐿 ′ = 0.16. dent function 𝐹𝑘, where 𝑟 is the number of oracle queries 𝒫 * makes. Importantly, due to the repetition, the first-stage reduction component must simulate the 𝖫𝗈𝖼𝖺𝗅𝗂𝗓𝖾 experiment from the beginning of time up through checkpoint 𝑖 ⋆ − 1, thus ensurin… view at source ↗
read the original abstract

While quantum position verification aims to certify a prover's location using quantum information, existing security definitions only guarantee that part of the successful adversarial party is in the claimed location. This leaves open the possibility that a distributed team of adversaries can jointly simulate a prover in a way that defeats the intended meaning of ``being at a location'' in position-based cryptography. We introduce stronger notions of position verification that we call quantum localization, which requires that there is a specified, unclonable state at the verified spacetime point -- and that this state can be found nowhere else. We show that quantum localization leads naturally to a meaningful notion of trajectory verification, in which quantum information is verifiably tracked through space and time. We construct quantum localization and trajectory verification protocols using quantum anchor states, which generalize coset states from unclonable cryptography. The security of our schemes is proven in the classical oracle (i.e. ideal obfuscation) model, which can be heuristically instantiated in the plain model using post-quantum indistinguishability obfuscation. We also introduce and instantiate the concept of functionality localization, which guarantees that the adversary has the ability to compute a secret function at the verified spacetime point, and this function cannot be computed anywhere else. This raises the intriguing possibility of localizing computational capabilities in space and time. More broadly, we believe our notions of quantum localization and our feasibility results provide stronger foundations for position-based cryptography.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces quantum localization as a stronger notion of position verification requiring a specified unclonable quantum state to be present at a verified spacetime point and nowhere else. It constructs protocols using quantum anchor states (generalizing coset states from unclonable cryptography), proves security in the classical oracle (ideal obfuscation) model, and extends the framework to trajectory verification (tracking quantum information through space and time) and functionality localization (localizing the ability to compute a secret function). The oracle-model security is described as heuristically instantiable in the plain model via post-quantum indistinguishability obfuscation, with the goal of providing stronger foundations for position-based cryptography.

Significance. If the results hold, the work strengthens position-based cryptography by moving from partial location guarantees to verifiable localization of specific unclonable states and computational capabilities. The quantum anchor states construction and oracle-model feasibility results supply a concrete technical advance with potential for applications in verifiable quantum information tracking.

major comments (2)
  1. [Abstract] Abstract: the central claim that quantum localization enforces an unclonable state 'at the verified spacetime point -- and that this state can be found nowhere else' rests on protocols whose security is established exclusively in the classical oracle model. The manuscript states that this 'can be heuristically instantiated in the plain model using post-quantum indistinguishability obfuscation' but supplies no reduction showing that the unclonability property survives the transition; quantum adversaries may exploit gaps (e.g., superposition queries or entanglement across locations) between oracle and concrete obfuscator behavior.
  2. [Security definitions and constructions] Security definitions and constructions: the definition of quantum localization (and its extension to trajectory verification) requires that the specified state cannot be found elsewhere, yet the provided details do not address whether a distributed adversarial team can jointly simulate the quantum anchor state without violating the oracle-model assumptions, leaving the 'nowhere else' guarantee load-bearing but unverified in the plain model.
minor comments (1)
  1. [Abstract] Abstract: the term 'quantum anchor states' is introduced without a one-sentence gloss or pointer to the defining section, which would improve immediate readability for readers unfamiliar with coset-state generalizations.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading and valuable feedback on the security model. We address the major comments point by point below, proposing clarifications to the manuscript where the concerns identify areas for improved precision.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that quantum localization enforces an unclonable state 'at the verified spacetime point -- and that this state can be found nowhere else' rests on protocols whose security is established exclusively in the classical oracle model. The manuscript states that this 'can be heuristically instantiated in the plain model using post-quantum indistinguishability obfuscation' but supplies no reduction showing that the unclonability property survives the transition; quantum adversaries may exploit gaps (e.g., superposition queries or entanglement across locations) between oracle and concrete obfuscator behavior.

    Authors: We agree that all formal security proofs, including the unclonability and 'nowhere else' properties, are established exclusively in the classical oracle model. The manuscript already qualifies the plain-model instantiation as heuristic and does not claim a formal reduction. To address the concern, we will revise the abstract and add a dedicated paragraph in the introduction to explicitly note that no reduction is provided, that the plain-model security remains conjectural, and that potential gaps (such as those arising from concrete obfuscator behavior) are not ruled out. This strengthens the presentation without altering the technical results. revision: yes

  2. Referee: [Security definitions and constructions] Security definitions and constructions: the definition of quantum localization (and its extension to trajectory verification) requires that the specified state cannot be found elsewhere, yet the provided details do not address whether a distributed adversarial team can jointly simulate the quantum anchor state without violating the oracle-model assumptions, leaving the 'nowhere else' guarantee load-bearing but unverified in the plain model.

    Authors: The security definitions and proofs for quantum localization (including trajectory verification) establish the 'nowhere else' guarantee against distributed adversaries in the classical oracle model, where the ideal obfuscation oracle enforces the required unclonability properties. We will expand the security definitions section to include an explicit statement clarifying the model in which the guarantees hold and to discuss that the plain-model version inherits the heuristic nature of the iO instantiation. This addresses the load-bearing aspect by making the model dependence more transparent. revision: partial

standing simulated objections not resolved
  • A formal reduction establishing that the unclonability and 'nowhere else' properties survive instantiation with a concrete post-quantum indistinguishability obfuscator (accounting for quantum adversaries, superposition queries, and entanglement across locations).

Circularity Check

0 steps flagged

No circularity; new definitions and model-based security proofs are independent of inputs

full rationale

The paper defines quantum localization as requiring a specified unclonable state at a verified spacetime point and nowhere else, constructs protocols via quantum anchor states (generalizing coset states), and proves security explicitly in the classical oracle model while noting a heuristic plain-model instantiation via post-quantum iO. No quoted steps reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations; the derivation chain remains self-contained within the stated model assumptions without renaming known results or smuggling ansatzes.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

Based solely on abstract; full paper may contain additional parameters or assumptions. Quantum anchor states are presented as a generalization rather than a fully independent invention.

axioms (2)
  • domain assumption Security holds in the classical oracle model of ideal obfuscation
    Invoked for proving security of the localization and trajectory protocols.
  • domain assumption Post-quantum indistinguishability obfuscation exists for heuristic instantiation
    Used to bridge the oracle model to the plain model.
invented entities (1)
  • quantum anchor states no independent evidence
    purpose: Basis for constructing quantum localization and trajectory verification protocols
    Generalizes coset states from unclonable cryptography; introduced to achieve the new localization properties.

pith-pipeline@v0.9.1-grok · 5797 in / 1335 out tokens · 34695 ms · 2026-06-28T22:21:39.445938+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

  1. [1]

    A Modular Approach to Unclonable Cryp- tography

    DOI: 10.1109/CCC.2009.42 . URL: https://doi.org/10.1109/CCC.2009.42 (cit. on pp. 9, 70). 85 [AB24] Prabhanjan Ananth and Amit Behera. “A Modular Approach to Unclonable Cryp- tography”. In: Advances in Cryptology – CRYPTO 2024: 44th Annual International Cryp- tology Conference, Santa Barbara, CA, USA, August 18–22, 2024, Proceedings, Part VII . 2024, pp. 3...

    work page doi:10.1109/ccc.2009.42 2009

  2. [2]

    Quantum Tokens for Digital Signatures

    URL: https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS. 2022.15 (cit. on p. 10). [BS23] Shalev Ben-David and Or Sattath. “Quantum Tokens for Digital Signatures”. In: Quantum 7 (2023), p. 901. DOI: 10 . 22331 / q - 2023 - 01 - 19 - 901. URL: https : / / doi.org/10.22331/q-2023-01-19-901 (cit. on p. 9). [CG24] Andrea Coladangelo and Sam Gunn. ...

    work page doi:10.4230/lipics.itcs 2022

  3. [3]

    How to record quantum queries, and applications to quantum in- differentiability

    DOI: 10.1007/978-3-642-32009-5_44 (cit. on p. 59). [Zha19] Mark Zhandry. “How to record quantum queries, and applications to quantum in- differentiability”. In:Annual International Cryptology Conference. Springer. 2019, pp. 239– 268 (cit. on pp. 18, 23, 24). 88 [Zha21] Mark Zhandry. “How to Construct Quantum Random Functions”. In: J. ACM 68.5 (2021). DOI:...

    work page doi:10.1007/978-3-642-32009-5_44 2019