arXiv subjects

Florian Speelman

Publications and source records attributed to Florian Speelman.

At least 19 recordsLinked to original sources

arXiv2026

Equivalence of non-local computation tasks beyond Clifford operations

Non-local quantum computation (NLQC) studies how two collaborating players can implement channels on distributed systems using a single simultaneous round of quantum communication and shared entanglement. NLQC has applications in diverse areas, ranging from quantum position-verification to quantum gravity. Recently, it has been realized that the relationships among families of NLQC tasks are highly structured: many seemingly distinct tasks are related by reductions, wherein implementations of one task can be used to efficiently implement a second task. This is analogous to the notion of reduction in complexity theory, and reveals the relative hardness of NLQC tasks. In this work we continue the study of reductions among NLQC tasks. We focus on NLQC examples of the greatest interest in quantum position-verification; in particular examples involving large classical inputs and fixed-size quantum inputs, since these constitute the most feasible protocols for position-verification schemes. Within this setting, we find many new relationships among NLQC tasks. For instance, protocols for the simplest example of redirecting a quantum system based on a classical control imply protocols for controlled single qubit measurements in arbitrary bases, the controlled application of any Clifford unitary, and even the controlled application of any unitary of the form $U=C_1DC_0$ with $D$ an arbitrary diagonal unitary and $C_0, C_1$ Clifford circuits. This implies that many feasible position-verification schemes have the same asymptotic scaling for their entanglement cost, and hence a similar level of security. Our techniques rely on ideas from gate teleportation and measurement based quantum computation, among other areas, bringing several new strategies into NLQC which may be of independent interest.

quant-ph↗

arXiv2026

Arbitrarily Loss-Tolerant Quantum Position Verification in a Single Execution

Quantum position verification (QPV) seeks to certify the spatial location of an untrusted prover, but is challenged fundamentally by entanglement-based attacks and experimentally by photon loss. Both issues were addressed separately in different works and were simultaneously resolved for sequentially repeated protocols in \textit{Phys.\ Rev.\ Lett.}\ \textbf{135},~260801 via a commitment-based modification that renders security independent of transmission losses. However, single-execution protocols are preferable in practice, and the original techniques do not extend to the parallel setting due to their reliance on sequential structure. We overcome this by utilizing different techniques based on no-signalling correlations, lifting the commitment modification to the parallel regime while preserving the security guarantees of the underlying QPV protocol. Applying this to a BB84-based QPV protocol suitable for near-term implementation and secure against bounded-entanglement adversaries, we prove that fixing a threshold~$k$ on the number of successfully committed qubits yields an adversarial acceptance probability that decays exponentially in~$k$. The resulting protocol maintains robustness to noise levels of up to~$3.7\%$ and remains secure under arbitrarily slow quantum communication, as does the original protocol. This yields the first fully loss-tolerant single-shot QPV protocol secure against entangled attackers, making QPV feasible over arbitrary distances. Finally, we refine the sequential analysis and obtain improved quantitative parameters for experimental implementations.

quant-ph↗

arXiv2026

Making Existing Quantum Position Verification Protocols Secure Against Arbitrary Transmission Loss

Signal loss poses a significant threat to the security of quantum cryptography when the chosen protocol lacks loss-tolerance. In quantum position verification (QPV) protocols, even relatively small loss rates can compromise security. The goal is thus to find protocols that remain secure under practically achievable loss rates. In this work, we modify the usual structure of QPV protocols and prove that this modification makes the potentially high transmission loss between the verifiers and the prover security-irrelevant for a class of protocols that includes a practically-interesting candidate protocol inspired by the BB84 protocol ($\mathrm{QPV}_{\mathrm{BB84}}^{f}$). This modification, which involves photon presence detection, a small time delay at the prover, and a commitment to play before proceeding, reduces the overall loss rate to just the prover's laboratory. The adapted protocol c-$\mathrm{QPV}_{\mathrm{BB84}}^{f}$ then becomes a practically feasible QPV protocol with strong security guarantees, even against attackers using adaptive strategies. As the loss rate between the verifiers and prover is mainly dictated by the distance between them, secure QPV over longer distances becomes possible. We also show possible implementations of the required photon presence detection, making c-$\mathrm{QPV}_{\mathrm{BB84}}^{f}$ a protocol that solves all major practical issues in QPV. Finally, we discuss experimental aspects and give parameter estimations.

quant-ph↗

arXiv2025

Fine-Grained Complexity via Quantum Natural Proofs

Buhrman, Patro, and Speelman presented a framework of conjectures that together form a quantum analogue of the strong exponential-time hypothesis and its variants. They called it the QSETH framework. In this paper, using a notion of quantum natural proofs (built from natural proofs introduced by Razborov and Rudich), we show how part of the QSETH conjecture that requires properties to be `compression oblivious' can in many cases be replaced by assuming the existence of quantum-secure pseudorandom functions, a standard hardness assumption. Combined with techniques from Fourier analysis of Boolean functions, we show that properties such as PARITY and MAJORITY are compression oblivious for certain circuit class $Λ$ if subexponentially secure quantum pseudorandom functions exist in $Λ$, answering an open question in [Buhrman-Patro-Speelman 2021].

quant-ph↗

arXiv2025

QSETH strikes again: finer quantum lower bounds for lattice problem, strong simulation, hitting set problem, and more

While seemingly undesirable, it is not a surprising fact that there are certain problems for which quantum computers offer no computational advantage over their respective classical counterparts. Moreover, there are problems for which there is no `useful' computational advantage possible with the current quantum hardware. This situation however can be beneficial if we don't want quantum computers to solve certain problems fast - say problems relevant to post-quantum cryptography. In such a situation, we would like to have evidence that it is difficult to solve those problems on quantum computers; but what is their exact complexity? To do so one has to prove lower bounds, but proving unconditional time lower bounds has never been easy. As a result, resorting to conditional lower bounds has been quite popular in the classical community and is gaining momentum in the quantum community. In this paper, by the use of the QSETH framework [Buhrman-Patro-Speelman 2021], we are able to understand the quantum complexity of a few natural variants of CNFSAT, such as parity-CNFSAT or counting-CNFSAT, and also are able to comment on the non-trivial complexity of approximate-#CNFSAT; both of these have interesting implications about the complexity of (variations of) lattice problems, strong simulation and hitting set problem, and more. In the process, we explore the QSETH framework in greater detail than was (required and) discussed in the original paper, thus also serving as a useful guide on how to effectively use the QSETH framework.

quant-ph↗

arXiv2025

Single-qubit loss-tolerant quantum position verification protocol secure against entangled attackers

Protocols for quantum position verification (QPV) which combine classical and quantum information are insecure in the presence of loss. We study the exact loss-tolerance of the most popular protocol for QPV, which is based on BB84 states, and generalizations of this protocol. By bounding the winning probabilities of a variant of the monogamy-of-entanglement game using semidefinite programming (SDP), we find tight bounds for the relation between loss and error for these extended non-local games. These new bounds enable the usage of QPV protocols using more-realistic experimental parameters. We show how these results transfer to the variant protocol which combines $n$ bits of classical information with a single qubit, thereby exhibiting a protocol secure against a linear amount of entanglement (in the classical information $n$) even in the presence of a moderate amount of photon loss. Moreover, this protocol stays secure even if the photon encoding the qubit travels arbitrarily slow in an optical fiber. We also extend this analysis to the case of more than two bases, showing even stronger loss-tolerance for that case. Finally, since our semi-definite program bounds a monogamy-of-entanglement game, we describe how they can also be applied to improve the analysis of one-sided device-independent QKD protocols.

quant-ph↗

arXiv2025

Quantum Catalytic Space

Space complexity is a key field of study in theoretical computer science. In the quantum setting there are clear motivations to understand the power of space-restricted computation, as qubits are an especially precious and limited resource. Recently, a new branch of space-bounded complexity called catalytic computing has shown that reusing space is a very powerful computational resource, especially for subroutines that incur little to no space overhead. While quantum catalysis in an information theoretic context, and the power of ``dirty'' qubits for quantum computation, has been studied over the years, these models are generally not suitable for use in quantum space-bounded algorithms, as they either rely on specific catalytic states or destroy the memory being borrowed. We define the notion of catalytic computing in the quantum setting and show a number of initial results about the model. First, we show that quantum catalytic logspace can always be computed quantumly in polynomial time; the classical analogue of this is the largest open question in catalytic computing. This also allows quantum catalytic space to be defined in an equivalent way with respect to circuits instead of Turing machines. We also prove that quantum catalytic logspace can simulate log-depth threshold circuits, a class which is known to contain (and believed to strictly contain) quantum logspace, thus showcasing the power of quantum catalytic space. Finally we show that both unitary quantum catalytic logspace and classical catalytic logspace can be simulated in the one-clean qubit model.

quant-ph↗

arXiv2025

Lossy-and-Constrained Extended Non-Local Games with Applications to Quantum Cryptography

Extended non-local games are a generalization of monogamy-of-entanglement games, played by two quantum parties and a quantum referee that performs a measurement on their local quantum system. Along the lines of the NPA hierarchy, the optimal winning probability of those games can be upper bounded by a hierarchy of semidefinite programs (SDPs) converging to the optimal value. Here, we show that if one extends such games by considering constraints and loss, motivated by experimental errors and loss through quantum communication, the convergence of the SDPs to the optimal value still holds. We give applications of this result, and we compute SDPs that show tighter security of protocols for relativistic bit commitment, quantum key distribution, and quantum position verification.

quant-ph↗

arXiv2025

Quantum position verification in one shot: parallel repetition of the $f$-BB84 and $f$-routing protocols

Quantum position verification (QPV) aims to verify an untrusted prover's location by timing communication with them. To reduce uncertainty, it is desirable for this verification to occur in a single round. However, previous protocols achieving one-round secure QPV had critical drawbacks: attackers pre-sharing an EPR pair per qubit could perfectly break them, and their security depended on quantum information traveling at the speed of light in vacuum, a major experimental challenge in quantum networks. In this work, we prove that a single round of interaction suffices for secure position verification while overcoming these limitations. We show that security for a one-round protocol can rely only on the size of the classical information rather than quantum resources, making implementation more feasible, even with a qubit error tolerance of up to 3.6%, which is experimentally achievable with current technology -- and showing that the timing constraints have to apply only to classical communication. In short, we establish parallel repetition of the $f$-BB84 and $f$-routing QPV protocols. As a consequence of our techniques, we also demonstrate an order-of-magnitude improvement in the error tolerance for the sequential repetition version of these protocols, compared to the previous bounds of Nature Physics 18, 623-626 (2022).

quant-ph↗

arXiv2025

Towards experimental demonstration of quantum position verification using true single photons

The geographical position can be a good credential for authentication of a party, this is the basis of position-based cryptography - but classically this cannot be done securely without physical exchange of a private key. However, recently, it has been shown that by combining quantum mechanics with the speed of light limit of special relativity, this might be possible: quantum position verification. Here we demonstrate experimentally a protocol that uses two-photon Hong-Ou-Mandel interference at a beamsplitter, which, in combination with two additional beam splitters and 4 detectors is rendering the protocol resilient to loss. With this we are able to show first results towards an experimental demonstration of quantum position verification.

quant-ph↗

arXiv2024

Port-Based State Preparation and Applications

We introduce Port-Based State Preparation (PBSP), a teleportation task where Alice holds a complete classical description of the target state and Bob's correction operations are restricted to only tracing out registers. We show a protocol that implements PBSP with error decreasing exponentially in the number of ports, in contrast to the polynomial trade-off for the related task of Port-Based Teleportation, and we prove that this is optimal when a maximally entangled resource state is used. As an application, we introduce approximate Universal Programmable Hybrid Processors (UPHP). Here the goal is to encode a unitary as a quantum state, and the UPHP can apply this unitary to a quantum state when knowing its classical description. We give a construction that needs strictly less memory in terms of dimension than the optimal approximate Universal Programmable Quantum Processor achieving the same error. Additionally, we provide lower bounds for the optimal trade-off between memory and error of UPHPs.

quant-ph↗

arXiv2024

A quantum cloning game with applications to quantum position verification

We introduce a quantum cloning game in which $k$ separate collaborative parties receive a classical input, determining which of them has to share a maximally entangled state with an additional party (referee). We provide the optimal winning probability of such a game for every number of parties $k$, and show that it decays exponentially when the game is played $n$ times in parallel. These results have applications to quantum cryptography, in particular in the topic of quantum position verification, where we show security of the routing protocol (played in parallel), and a variant of it, in the random oracle model.

quant-ph↗

arXiv2024

Fully Characterizing Lossy Catalytic Computation

A catalytic machine is a model of computation where a traditional space-bounded machine is augmented with an additional, significantly larger, "catalytic" tape, which, while being available as a work tape, has the caveat of being initialized with an arbitrary string, which must be preserved at the end of the computation. Despite this restriction, catalytic machines have been shown to have surprising additional power; a logspace machine with a polynomial length catalytic tape, known as catalytic logspace ($CL$), can compute problems which are believed to be impossible for $L$. A fundamental question of the model is whether the catalytic condition, of leaving the catalytic tape in its exact original configuration, is robust to minor deviations. This study was initialized by Gupta et al. (2024), who defined lossy catalytic logspace ($LCL[e]$) as a variant of $CL$ where we allow up to $e$ errors when resetting the catalytic tape. They showed that $LCL[e] = CL$ for any $e = O(1)$, which remains the frontier of our understanding. In this work we completely characterize lossy catalytic space ($LCSPACE[s,c,e]$) in terms of ordinary catalytic space ($CSPACE[s,c]$). We show that $$LCSPACE[s,c,e] = CSPACE[Θ(s + e \log c), Θ(c)]$$ In other words, allowing $e$ errors on a catalytic tape of length $c$ is equivalent, up to a constant stretch, to an equivalent errorless catalytic machine with an additional $e \log c$ bits of ordinary working memory. As a consequence, we show that for any $e$, $LCL[e] = CL$ implies $SPACE[e \log n] \subseteq ZPP$, thus giving a barrier to any improvement beyond $LCL[O(1)] = CL$. We also show equivalent results for non-deterministic and randomized catalytic space.

cs.CC↗

arXiv2024

A Quantum Computing Approach for Multi-robot Coverage Path Planning

This paper tackles the multi-vehicle Coverage Path Planning (CPP) problem, crucial for applications like search and rescue or environmental monitoring. Due to its NP-hard nature, finding optimal solutions becomes infeasible with larger problem sizes. This motivates the development of heuristic approaches that enhance efficiency even marginally. We propose a novel approach for exploring paths in a 2D grid, specifically designed for easy integration with the Quantum Alternating Operator Ansatz (QAOA), a powerful quantum heuristic. Our contribution includes: 1) An objective function tailored to solve the multi-vehicle CPP using QAOA. 2) Theoretical proofs guaranteeing the validity of the proposed approach. 3) Efficient construction of QAOA operators for practical implementation. 4) Resource estimation to assess the feasibility of QAOA execution. 5) Performance comparison against established algorithms like the Depth First Search. This work paves the way for leveraging quantum computing in optimizing multi-vehicle path planning, potentially leading to real-world advancements in various applications.

quant-ph↗

arXiv2024

Relating non-local quantum computation to information theoretic cryptography

Non-local quantum computation (NLQC) is a cheating strategy for position-verification schemes, and has appeared in the context of the AdS/CFT correspondence. Here, we connect NLQC to the wider context of information theoretic cryptography by relating it to a number of other cryptographic primitives. We show one special case of NLQC, known as $f$-routing, is equivalent to the quantum analogue of the conditional disclosure of secrets (CDS) primitive, where by equivalent we mean that a protocol for one task gives a protocol for the other with only small overhead in resource costs. We further consider another special case of position verification, which we call coherent function evaluation (CFE), and show CFE protocols induce similarly efficient protocols for the private simultaneous message passing (PSM) scenario. By relating position-verification to these cryptographic primitives, a number of results in the cryptography literature give new implications for NLQC, and vice versa. These include the first sub-exponential upper bounds on the worst case cost of $f$-routing of $2^{O(\sqrt{n\log n})}$ entanglement, the first example of an efficient $f$-routing strategy for a problem believed to be outside $P/poly$, linear lower bounds on entanglement for CDS in the quantum setting, linear lower bounds on communication cost of CFE, and efficient protocols for CDS in the quantum setting for functions that can be computed with quantum circuits of low $T$ depth.

quant-ph↗

arXiv2024

Continuous-variable Quantum Position Verification secure against entangled attackers

Motivated by the fact that coherent states may offer practical advantages it was recently shown that a continuous-variable (CV) quantum position verification (QPV) protocol using coherent states could be securely implemented if and only if attackers do not pre-share any entanglement. In the discrete-variable (DV) analogue of that protocol it was shown that modifying how the classical input information is sent from the verifiers to the prover leads to a favourable scaling in the resource requirements for a quantum attack. In this work, we show that similar conclusions can be drawn for CV-QPV. By adding extra classical information of size $n$ to a CV-QPV protocol, we show that the protocol, which uses a coherent state and classical information, remains secure, even if the quantum information travels arbitrarily slow, against attackers who pre-share CV (entangled) states with a linear (in $n$) cutoff at the photon number. We show that the protocol remains secure for certain attenuation and excess noise.

quant-ph↗

arXiv2023

Oblivious Transfer from Zero-Knowledge Proofs, or How to Achieve Round-Optimal Quantum Oblivious Transfer and Zero-Knowledge Proofs on Quantum States

We provide a generic construction to turn any classical Zero-Knowledge (ZK) protocol into a composable (quantum) oblivious transfer (OT) protocol, mostly lifting the round-complexity properties and security guarantees (plain-model/statistical security/unstructured functions...) of the ZK protocol to the resulting OT protocol. Such a construction is unlikely to exist classically as Cryptomania is believed to be different from Minicrypt. In particular, by instantiating our construction using Non-Interactive ZK (NIZK), we provide the first round-optimal (2-message) quantum OT protocol secure in the random oracle model, and round-optimal extensions to string and k-out-of-n OT. At the heart of our construction lies a new method that allows us to prove properties on a received quantum state without revealing additional information on it, even in a non-interactive way, without public-key primitives, and/or with statistical guarantees when using an appropriate classical ZK protocol. We can notably prove that a state has been partially measured (with arbitrary constraints on the set of measured qubits), without revealing any additional information on this set. This notion can be seen as an analog of ZK to quantum states, and we expect it to be of independent interest as it extends complexity theory to quantum languages, as illustrated by the two new complexity classes we introduce, ZKstatesQIP and ZKstatesQMA.

quant-ph↗

arXiv2023

Security of a Continuous-Variable based Quantum Position Verification Protocol

In this work we study quantum position verification with continuous-variable quantum states. In contrast to existing discrete protocols, we present and analyze a protocol that utilizes coherent states and its properties. Compared to discrete-variable photonic states, coherent states offer practical advantages since they can be efficiently prepared and manipulated with current technology. We prove security of the protocol against any unentangled attackers via entropic uncertainty relations, showing that the adversary has more uncertainty than the honest prover about the correct response as long as the noise in the quantum channel is below a certain threshold. Additionally, we show that attackers who pre-share one continuous-variable EPR pair can break the protocol.

quant-ph↗