Awesome Position-Based Quantum Cryptography

This is a curated list of papers on position-based quantum cryptography (PBQC). The goal is to build a categorised community-driven always up-to-date literature overview of this growing field.

QPV = Quantum Position Verification

QPA = Quantum Position-based Authentication

PB-QKD = Position-based Quantum Key Distribution

Contents

• Classical Impossibility
• First Protocols
• Universal Attacks on QPV
• Ways Around the Universal Attacks on QPV
• Conjectured Exponential Lower Bound
• Quantum Position-based Authentication
• Towards Understanding NLQC
• Towards Practicality
• Experiments

Classical Impossibility

• Position-based cryptography (2009) - Establishes classical impossibility of position-based cryptography in the vanilla model. Explores possibility in the bounded-storage model.

First Protocols

• Tagging systems (2006) - Introduces QPV under the name of 'quantum tagging'.
• Location-dependent communications using quantum entanglement (2010) - Introduces QPV in the academic literature, but incorrectly claims unconditional security. Studies QPV based on Bell states.
• Quantum location verification in noisy channels (2010) - Studies QPV based on Bell states, GHZ states and entanglement swapping. Studies the effect of noise/decoherence.
• Quantum tagging: Authenticating location via quantum information and relativistic signalling constraints (2011) - Introduces a rooster of different QPV protocols like BB84 QPV, $f$-routing, $f$-BB84 QPV and variations of them. Mentions entanglement-based attacks on some of them.

BB84 QPV and Generalisations

• Position-based quantum cryptography: Impossibility and constructions (2011) - Shows security against unentangled attacks.
• A monogamy-of-entanglement game with applications to device-independent quantum cryptography (2013) - Shows a tight upper bound for unentangled attacks, parallel repetition and a linear lower bound for the repeated protocol.
• Practical position-based quantum cryptography (2015) - Considers the case where the two input bases are related by a unitary $U$.
• A tight lower bound for the BB84-states quantum-position-verification protocol (2015) - Gives essentially tight lower bound for attacks with classical communication.
• Loss-tolerant position-based quantum cryptography (2015) - Generalises BB84 QPV to more input bases and notes better loss tolerance properties because of it. Also discusses using decoy states and continuous variables for BB84 QPV.
• Position-based quantum cryptography and catalytic computation (2016) - Chapter 5 independently generalises BB84 QPV to more input bases. Chapter 4 provides an efficient attack on the protocol based on interleaved unitaries.
• Breaking simple quantum position verification protocols with little entanglement (2020) - Considers the case when the input bases are related by different angles and shows dimension-dependent attacks depending on the angle. Notably, they show the angle $\pi/6$ (outside the Clifford hierarchy) can be attacked with a 6-dimensional resource state.
• Single-qubit loss-tolerant quantum position verification protocol secure against entangled attackers (2023) - Tightly characterises the secure region of the protocol depending on the loss and error rates.
• Security of a continuous-variable based quantum position verification protocol (2023) - Generalises the protocol to continuous variable inputs and shows security against unentangled attacks depending on loss and noise rates.
• Perfect cheating is impossible for single-qubit position verification (2024) - Considers a generalisation where the input qubits are eigenstates of a $\mathbb{C}^2$ projector chosen uniformly at random. Shows that no finite-dimensional resource state can perfectly attack this protocol.

$f$-routing

• The garden-hose model (2013) - Studies attacks on $f$-routing and introduces garden-hose complexity to connect attacks on $f$-routing to complexity theory. Provides many first results regarding that connection, for example that any $f \in \mathsf{L}$ (with pre-processing) can be attacked efficiently.