A single-qubit position verification protocol that is secure against multi-qubit attacks

Bluhm, Andreas; Christandl, Matthias; Speelman, Florian

doi:10.48550/arxiv.2104.06301

Cited by 5 publications

(14 citation statements)

References 11 publications

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“…In this work we gave the first lower bound on entanglement from complexity. Qualitatively, this is different from existing bounds, which are either for specific tasks [18,42] or specific families of tasks [43]. While it is interesting a lower bound of this type exists, the bound we have given is much weaker than suggested by our 'strong' complexity-entanglement conjecture.…”

Section: Improved Lower Bounds On Entanglementcontrasting

confidence: 90%

“…Assuming classical computation is easy and storing (even polynomial) entanglement is hard then still leads to a gap between the difficulty of honest and dishonest strategies. For work in this direction see [43].…”

Section: Discussionmentioning

confidence: 99%

“…There are a few tasks where lower bounds on the resources needed in non-local computation have been proven [17,18,42,43]. All known bounds that do not make assumptions about the protocol used are linear, with each different bound applying for a different choice of task.…”

Section: Definition 5 N Lqc Amentioning

confidence: 99%

“…( 20) with α = 1 using monogamy games. Similarly, all of the bounds in [17,18,43] are linear with α < 1.…”

Section: Definition 5 N Lqc Amentioning

confidence: 99%

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Complexity and entanglement in non-local computation and holography

May¹

2022

Preprint

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Does gravity constrain computation?We study this question using the AdS/CFT correspondence, where computation in the presence of gravity can be related to non-gravitational physics in the boundary theory. In AdS/CFT, computations which happen locally in the bulk are implemented in a particular non-local form in the boundary, which in general requires distributed entanglement. In more detail, we recall that for a large class of bulk subregions the area of a surface called the ridge is equal to the mutual information available in the boundary to perform the computation non-locally. We then argue the complexity of the local operation controls the amount of entanglement needed to implement it non-locally, and in particular complexity and entanglement cost are related by a polynomial. If this relationship holds, gravity constrains the complexity of operations within these regions to be polynomial in the area of the ridge.

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Section: Improved Lower Bounds On Entanglementcontrasting

confidence: 90%

Section: Discussionmentioning

confidence: 99%

Section: Definition 5 N Lqc Amentioning

confidence: 99%

“…( 20) with α = 1 using monogamy games. Similarly, all of the bounds in [17,18,43] are linear with α < 1.…”

Section: Definition 5 N Lqc Amentioning

confidence: 99%

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Complexity and entanglement in non-local computation and holography

May¹

2022

Preprint

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“…All previous protocols in the standard model (as opposed to the QROM) are not known to be secure even against an arbitrary polynomial amount of entanglement, and any protocol can be broken with an exponential amount of entanglement [BCF + 14, BK11]. Furthermore, the position verification protocols that are secure against any polynomial amount of entanglement are all proven in the QROM, either explicitly [Unr14] or implicitly via considering a random function in the security proof [BCS21].…”

Section: Our Resultsmentioning

confidence: 99%

Beating Classical Impossibility of Position Verification

Liu

Liu²,

Qian

2021

Preprint

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Chandran et al. (SIAM J. Comput. '14) formally introduced the cryptographic task of position verification, where they also showed that it cannot be achieved by classical protocols. In this work, we initiate the study of position verification protocols with classical verifiers. We identify that proofs of quantumness (and thus computational assumptions) are necessary for such position verification protocols. For the other direction, we adapt the proof of quantumness protocol by Brakerski et al. (FOCS '18) to instantiate such a position verification protocol. As a result, we achieve classically verifiable position verification assuming the quantum hardness of Learning with Errors.Along the way, we develop the notion of 1-of-2 non-local soundness for the framework of 1-of-2 puzzles, first introduced by Radian and Sattath (AFT '19), which can be viewed as a computational unclonability property. We show that 1-of-2 non-local soundness follows from the standard 2-of-2 soundness, which could be of independent interest.

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Geometry of Banach Spaces: A New Route Towards Position Based Cryptography

Junge

Kubicki

Palazuelos

et al. 2022

Commun. Math. Phys.

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In this work we initiate the study of position based quantum cryptography (PBQC) from the perspective of geometric functional analysis and its connections with quantum games. The main question we are interested in asks for the optimal amount of entanglement that a coalition of attackers have to share in order to compromise the security of any PBQC protocol. Known upper bounds for that quantity are exponential in the size of the quantum systems manipulated in the honest implementation of the protocol. However, known lower bounds are only linear. In order to deepen the understanding of this question, here we propose a position verification (PV) protocol and find lower bounds on the resources needed to break it. The main idea behind the proof of these bounds is the understanding of cheating strategies as vector valued assignments on the Boolean hypercube. Then, the bounds follow from the understanding of some geometric properties of particular Banach spaces, their type constants. Under some regularity assumptions on the former assignment, these bounds lead to exponential lower bounds on the quantum resources employed, clarifying the question in this restricted case. Known attacks indeed satisfy the assumption we make, although we do not know how universal this feature is. Furthermore, we show that the understanding of the type properties of some more involved Banach spaces would allow to drop out the assumptions and lead to unconditional lower bounds on the resources used to attack our protocol. Unfortunately, we were not able to estimate the relevant type constant. Despite that, we conjecture an upper bound for this quantity and show some evidence supporting it. A positive solution of the conjecture would lead to stronger security guarantees for the proposed PV protocol providing a better understanding of the question asked above.

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A single-qubit position verification protocol that is secure against multi-qubit attacks

Cited by 5 publications

References 11 publications

Complexity and entanglement in non-local computation and holography

Complexity and entanglement in non-local computation and holography

Beating Classical Impossibility of Position Verification

Geometry of Banach Spaces: A New Route Towards Position Based Cryptography

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