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
Establishes classical impossibility of position-based cryptography in the vanilla model. Explores possibility in the bounded-storage model.
Introduces QPV under the name of 'quantum tagging'.
Studies QPV based on Bell states, GHZ states and entanglement swapping. Studies the effect of noise/decoherence.
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.
Shows security against unentangled attacks.
Shows a tight upper bound for unentangled attacks, parallel repetition and a linear lower bound for the repeated protocol.
Considers the case where the two input bases are related by a unitary $U$.
Gives essentially tight lower bound for attacks with classical communication.
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.
Chapter 5 independently generalises BB84 QPV to more input bases. Chapter 4 provides an efficient attack on the protocol based on interleaved unitaries.
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.
Tightly characterises the secure region of the protocol depending on the loss and error rates.
Generalises the protocol to continuous variable inputs and shows security against unentangled attacks depending on loss and noise rates.
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.
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.
Shows a robust linear lower bound on the dimension of the attack resource state.
Provides a new attack on $f$-routing, connecting attacks to secret-sharing schemes and span programs, and showing that any $f \in \mathsf{Mod}_p\mathsf{L}$ (with pre-processing), for $p$ prime, can be attacked efficiently.
Connects $f$-routing to topics in classical cryptography, in particular conditional disclosure of secrets. Shows a sub-exponential upper bound for attacks for any $f$ and finds an $f$ that is believed to be outside of $\mathsf{P}$ (with pre-processing), but efficiently attacked.
Provides a lower bound in terms of the Schmidt-rank of the resource state for perfect attacks. Gives linear lower bounds for some concrete functions.
Provides a robust linear lower bound on the number of quantum gates/measurements needed to attack the inner product function.
Considers QPV in higher dimensions carefully and shows unconditional security in the random oracle model.
Shows a robust linear lower bound on the dimension of the attack resource state.
Tightly characterises the secure region of the protocol depending on the loss and error rates.
Introduces an extra commitment step into QPV and shows that for a class of protocols, involving $f$-BB84 QPV, this makes the transmission loss irrelevant for security. Argues $f$-BB84 is a practical QPV protocol.
Generalises $f$-BB84 QPV to continuous-variable inputs and shows analogous security statements as for finite-dimensional inputs.
Studies QPV based on Bell states, GHZ states and entanglement swapping. Studies the effect of noise/decoherence.
Studies a version of the protocol with separable inputs. Proves full loss tolerance and studies practical implementation based on decoy states.
Proves a 3/4 upper bound on the success probability of unentangled attacks.
The results in this paper imply a $\ln(2) \approx 0.69$ upper bound on the success probability of unentangled attacks.
Provides a protocol based on interleaved unitaries, conjecturing security. The protocol was broken efficiently later.
Considers BB84 QPV with non-simultaneous arrival times of input information at the prover (the basis being encoded in which side arrived first). Discusses the general port-based attack in this setting.
Gives an overview over the existing protocols at the time and mixes elements of them to obtain different variations of those protocols.
Defines a new protocol based on the SWAP test and studies it theoretically and practically.
Introduces an extra commitment step into QPV and shows that for a class of protocols this makes the transmission loss irrelevant for security.
Rigorously defines QPV and provides an general attack on all such QPV protocols using a doubly exponential amount of pre-shared EPR pairs in the number of input qubits.
Provides a general attack on QPV based on port-based teleportation, using an exponential amount of pre-shared EPR pairs in the number of input qubits. Also provides a QPV protocol with a provably linear lower bound.
Provides a general attack on QPV using an exponential amount of pre-shared EPR pairs in the number of T-gates or T-depth based on the circuit decomposition of the task unitary into Clifford+T gates.
Provides a general attack on QPV based on the geometric structure of a circuit decomposition of the task unitary. Is more efficient for certain classes of unitaries than previous general attacks.
Shows efficient attacks for certain classes, like the second level of the Clifford hierarchy.
Shows that any 2-qubit unitary can be attacked up to error $\varepsilon$ using $\log(1/\varepsilon)$ EPR pairs and that any hermitian bipartite binary controlled unitary can be attacked with 1 EPR pair. Shows logarithmic lower bound on entanglement entropy for general bipartite binary controlled unitary.
Considers QPV in the setting when the verifiers and the prover pre-share a secret. Shows that then QPV is unconditionally secure by indefinitely expanding the secret using QKD.
Shows unconditional security of $f$-BB84 QPV in the random oracle model.
Constructs a QPV protocol with only classical input and output information from the assumption that LWE is quantum-hard. Shows unconditional security in the random oracle model.
Provides a new protocol based on applying a phase unitary depending on the classical input information. Shows an exponential lower bound under a regularity assumption on the attack, and an exponential lower bound conditioned on an, as yet, unresolved Banach space geometry conjecture.
Provides a generic, but inefficient, construction to go from QPV to QPA to PB-QKD.
Provides more efficient extensions to QPA and PB-QKD in the random oracle model for $f$-BB84 QPV.
Improved analysis of how to use QPV to provide the authentication within QKD.
Considers more general quantum tasks than QPV.
Shows that if attackers share PR boxes, then any unitary can be attacked using only linear entanglement and a linear number of PR box uses.
Generalises the port-based attack to more general quantum tasks and spacetime circuits. Finds that the coarse causal structure of the task is the relevant property determining whether the task is doable non-locally.
Shows that any QPV protocol that can be broken unentangled with quantum communication, but is secure against classical communication attacks, can be transformed into one that is secure against quantum communication attacks. Also notes that if the signal loss is high enough any QPV protocol can be attacked efficiently by a trivial teleportation attack.
Notes that the necessary attack resource requirements are controlled by the entangled part of the task unitary. Shows that for tasks where one side is classical input information, a doubly-logarithmic (later improved to logarithmic) lower bound and exponential upper bound (in terms of any complexity measure of your choice of the entangled part of the task unitary) hold for attacks.
Connects NLQC to some protocols in classical cryptography via $f$-routing.
Studies the difference between unentangled quantum and classical attacks on state discrimination QPV protocols and proves several results on that, for example that there is a separable state ensemble that can be perfectly discriminated with quantum communication, but not without.
Finds relations between a wide range of different NLQC tasks, including showing that $f$-routing and $f$-BB84 are equivalent, with a constant-overhead reduction between them.
Discusses and fills a loophole in the paper one above. Costructs an attacked based on simulating a holographic CFT and argues that, based on some assumptions, any polynomially complex unitary can be efficiently attacked.
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.
Studies Bell QPV with separable inputs. Proves full loss tolerance and studies practical implementation based on decoy states.
Defines a new protocol based on the SWAP test and studies it theoretically and practically. Argues that this protocol has practically versatile and robust properties.
Tightly characterises the secure region of BB84 QPV and $f$-BB84 QPV depending on the loss and error rates.
Generalises BB84 QPV to continuous variable inputs and shows security against unentangled attacks depending on loss and noise rates.
Introduces an extra commitment step into QPV and shows that for a class of protocols, involving $f$-BB84 QPV, this makes the transmission loss irrelevant for security. Argues $f$-BB84 is a practical QPV protocol.
Delves into some technical hardware details of a practical QPV implementation.
Generalises $f$-BB84 QPV to continuous-variable inputs and shows analogous security statements as for finite-dimensional inputs.
A first demonstration experiment of QPV using the SWAP protocol, with single photons from a single semiconductor quantum dot in an optical microcavity.