In this thesis we explore position-based quantum cryptography zooming in on the task of position verification. In position verification, the idea is to use an individual's geographical location as a cryptographic credential. In practice, such protocols can authenticate that a message originated from a specific location or ensure that messages can only be read at a certain location. In a position-verification protocol, the limitations imposed by the speed of light, as described by special relativity, are used to verify that a party is at their claimed location. It has been shown that any QPV protocol can be broken by attackers that use an amount of entanglement exponential in the input size. However, from a practical point of view, not all is lost. We can still hope for QPV protocols that are secure in practice. This raises the problem of designing protocols that are secure in a practical setting. An important problem that arises is that of signal loss. Signal loss can be detrimental as it allows attackers to only answer on a subset of rounds. We investigate several questions related to the practical implementation of such protocols. We propose a new experimentally feasible protocol, which is fully loss-tolerant against attackers restricted to classical communication. Furthermore, we consider the role of allowing quantum communication with no pre-shared entanglement for attackers and show that this setting is strictly stronger than the classical one, indicating that allowing for quantum communication may break security. Conversely, we then show that any protocol secure against classical communication can be transformed into a protocol secure against quantum communication. Finally, we invert the picture, and consider the task of non-local quantum computation (NLQC), which corresponds to the operations of the attackers in a QPV protocol. We connect NLQC to the wider context of information-theoretic cryptography by relating it to a number of other cryptographic primitives.
In this thesis we explore position-based quantum cryptography zooming in on the task of position verification. In position verification, the idea is to use an individual's geographical location as a cryptographic credential. In practice, such protocols can authenticate that a message originated from a specific location or ensure that messages can only be read at a certain location. In a position-verification protocol, the limitations imposed by the speed of light, as described by special relativity, are used to verify that a party is at their claimed location. It has been shown that any QPV protocol can be broken by attackers that use an amount of entanglement exponential in the input size. However, from a practical point of view, not all is lost. We can still hope for QPV protocols that are secure in practice. This raises the problem of designing protocols that are secure in a practical setting. An important problem that arises is that of signal loss. Signal loss can be detrimental as it allows attackers to only answer on a subset of rounds. We investigate several questions related to the practical implementation of such protocols. We propose a new experimentally feasible protocol, which is fully loss-tolerant against attackers restricted to classical communication. Furthermore, we consider the role of allowing quantum communication with no pre-shared entanglement for attackers and show that this setting is strictly stronger than the classical one, indicating that allowing for quantum communication may break security. Conversely, we then show that any protocol secure against classical communication can be transformed into a protocol secure against quantum communication. Finally, we invert the picture, and consider the task of non-local quantum computation (NLQC), which corresponds to the operations of the attackers in a QPV protocol. We connect NLQC to the wider context of information-theoretic cryptography by relating it to a number of other cryptographic primitives.
This doctoral thesis explores quantum position verification (QPV)---a cryptographic task where one attempts to confirm someone’s geographical location. The core question that QPV aims to answer is: Are you truly at the location you claim to be? To achieve this, QPV combines two pillars of the fundamental laws of nature: (i) special relativity, which limits the speed at which information can travel to the speed of light in vacuum, and (ii) quantum mechanics, which governs the behavior of quantum particles in ways that defy intuition. QPV protocols rely on (i) timing communication between the entities involved in the protocol, and (ii) transmitting information encoded in quantum particles. However, quantum hackers may attempt to pretend to be at the claimed location while actually being elsewhere. This raises the critical question: Can one be certain that the claimed location is genuine and not forged by hackers? This thesis presents new advances toward a fundamental understanding of QPV, its security against powerful quantum hackers, and the feasibility of secure QPV protocols despite experimental challenges that, if exploited by hackers, can severely compromise their security. Furthermore, related to attacks on QPV protocols, this thesis analyzes quantum correlations that emerge in broader cryptographic primitives.
We study the role of quantum communication in attacks on quantum position verification. In this work, we construct the first known example of a QPV protocol that is provably secure against unentangled attackers restricted to classical communication, but can be perfectly attacked by local operations and a single round of simultaneous quantum communication indicating that allowing for quantum communication may break security. We also show that any protocol secure against classical communication can be transformed into a protocol secure against quantum communication. We further show, using arguments based on the monogamy of entanglement, that the task of Bell state discrimination cannot be done locally with a single round of quantum communication, not even probabilistically (when we allow attackers to say loss sometimes), making this the first fully loss-tolerant QPV task secure against quantum communication attacks. Finally, we observe that any multi-round QPV protocol can be attacked with a linear amount of entanglement if the loss is high enough.
Quantum position verification (QPV) aims to certify the location of an untrusted prover, but faces two major obstacles: fundamentally, entanglement-based attacks and, experimentally, photon loss. A commitment-based modification introduced in Phys. Rev. Lett. 135, 260801 addresses both in sequentially repeated protocols. Its security analysis, however, relies on the sequential structure and does not extend to parallel repetition. We use a different proof approach to establish security of the commitment modification for a parallel BB84-based QPV protocol. Against bounded-entanglement adversaries, the acceptance probability decays exponentially in the minimum number k of successfully committed qubits. The protocol tolerates arbitrary transmission loss and noise rates up to 3.7%, while allowing arbitrarily slow quantum communication. This yields a fully loss-tolerant, single-execution QPV protocol secure against bounded-entanglement attacks, removing transmission loss as a fundamental limitation on verification distance. We also revisit sequential repetition, correcting the treatment of conditioning on commitment and replacing the earlier conditional guarantee with an unconditional security bound, without the finite-size correction to the correctness gap. The resulting bound provides improved quantitative security parameters for experimental implementations.
This thesis deals with position-based quantum cryptography (PBQC), a type of quantum cryptography. More concretely, we focus on the design and study of quantum position verification (QPV) protocols, which act as a building block for PBQC. We prioritise the development of QPV protocols that are loss-tolerant, error-robust, and feasible with current or near-future technology, concentrating on photon-based protocols and linear-optical equipment. We also theoretically study different attack settings on QPV in the context of state discrimination, dealing with the interplay between non-locality and interaction. We introduce a new QPV protocol based on the SWAP test and Hong-Ou-Mandel interference and study it in detail regarding attacks and practical feasibility. We further provide a solution to a major practical issue of QPV -- signal loss. A minor modification of the standard structure of QPV, namely introducing a small time delay and a commitment to play from the honest prover, allows us to provably make the transmission loss between the verifiers and the honest party irrelevant for security for a class of QPV protocols. Moreover, we generalise and study QPV protocols in the continuous-variable setting. Exploring theoretical aspects of QPV attacks, we focus on the difference between quantum and classical communication. We show new bounds on existing protocols, construct protocols that can be attacked with quantum communication but not locally, show a separation between quantum and classical communication attacks on QPV, and derive a necessary condition on the attack error based on the structure of the QPV input ensemble.
A spacetime seal, a cryptographic guarantee that a digital event has occurred at an approved location and time, can augment a digital signature with location attestation for legal, financial, and regulatory use cases. In adversarial settings any purely classical realization of such a seal can be spoofed. Quantum position verification (QPV) offers a physics-based solution, exploiting the no-cloning theorem and the no-signaling principle to certify a party's spacetime coordinates. While the feasibility of QPV has been recently shown via entanglement- and coherent light-based protocols, achieving loss tolerance for these schemes substantially increases implementation complexity at metropolitan scales. Here, we introduce and experimentally demonstrate a loss-tolerant QPV (LT-QPV) protocol whose security is independent of channel loss. We prove finite-size security against quantum polynomial-time entangled adversaries in the quantum random oracle model instantiated with cryptographically secure hash functions. Implemented entirely with commercial off-the-shelf components, our system certifies position within 22 minutes of net data collection time against a restricted adversary, with a clear path to real-time certification (<1s) with upgraded hardware. Our architecture, requiring only a single quantum verifier node alongside classical infrastructure, is naturally compatible with metropolitan-area quantum networks, establishing the foundations for scalable, physics-backed spacetime certification as a deployable service.
Loss of inputs can be detrimental to the security of quantum position verification (QPV) protocols, as it may allow attackers to not answer on all played rounds, but only on those they perform well on. In this work, we study \textit{loss-tolerant} QPV protocols. We propose a new fully loss-tolerant protocol QPVSWAP, based on the SWAP test, with several desirable properties. The task of the protocol, which could be implemented using only a single beam splitter and two detectors, is to estimate the overlap between two input states. By formulating possible attacks as a semi-definite program (SDP), we prove full loss tolerance against unentangled attackers restricted to local operations and classical communication, and show that the attack probability decays exponentially under parallel repetition of rounds. We show that the protocol remains secure even if unentangled attackers are allowed to quantum communicate, making our protocol the first fully loss-tolerant protocol with this property. A detailed analysis under experimental conditions is conducted, showing that QPVSWAP remains fairly robust against equipment errors. We identify a necessary condition for security with errors and simulate one instance of our protocol with currently realistic experimental parameters, gathering that an attack success probability of ≤10−6 can be achieved by collecting just a few hundred conclusive protocol rounds.