arXiv subjects

Carla Ferradini

Publications and source records attributed to Carla Ferradini.

7 recordsLinked to original sources

arXiv2026

Error Correction in Lattice Quantum Electrodynamics with Quantum Reference Frames

Is gauge symmetry merely a redundancy in our description, or does it carry a deeper information-theoretic significance? Quantum error-correcting codes (QECCs) show that redundancy can serve as a resource for protecting information against noise. In this work, we ask whether gauge theories can be understood in similar terms, and make this idea concrete in lattice quantum electrodynamics (QED), building on and extending earlier works that established a bridge between gauge systems, stabilizer codes, and quantum reference frames (QRFs). For Abelian gauge groups, we show that explicit recovery operations can be constructed using group-theoretical methods for error sets determined by both ideal and non-ideal QRFs. Applied to lattice QED, this yields two QECC structures: one in the pure-gauge sector and one including fermions. We construct a gauge-field QRF based on spanning trees of the lattice and a fermionic field QRF from the matter field, thereby making explicit how physical information is encoded. While the syndromes of gauge-violating errors associated with constraint measurements are generically degenerate, QRFs resolve this degeneracy and single out families of correctable errors. This establishes lattice QED as a QECC beyond the stabilizer setting and shows concretely how gauge symmetry provides an encoding structure that supports error correction.

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arXiv2026

Emergent causal order and time direction: bridging causal models and tensor networks

Can the direction of time and the causal structure of space-time be inferred from operational principles? Causal models and tensor networks offer complementary perspectives: the former encodes cause-effect relations via directed graphs, with intrinsic ordering; the latter describes multipartite systems on undirected graphs, without presupposing directionality. We construct two-way mappings between these two frameworks, linking direction agnostic correlation functions and operational notions of signalling. This clarifies the operational meaning of causal influence in tensor networks and introduces discrete "space-time rotations'' of causal models which preserve signalling relations. Applying our framework to holographic tensor networks, we use tools from causal inference, like graph-separation, to analyse emergent causal structures. By permitting cyclic and indefinite causal structures, our results enable transfer of techniques across tensor networks and a range of causality frameworks.

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arXiv2025

Randomness from causally independent processes

We consider a pair of causally independent processes, modelled as the tensor product of two channels, acting on a possibly correlated input to produce random outputs X and Y. We show that, assuming the processes produce a sufficient amount of randomness, one can extract uniform randomness from X and Y. This generalizes prior results, which assumed that X and Y are (conditionally) independent. Note that in contrast to the independence of quantum states, the independence of channels can be enforced through spacelike separation. As a consequence, our results allow for the generation of randomness under more practical and physically justifiable assumptions than previously possible. We illustrate this with the example of device-independent randomness amplification, where we can remove the constraint that the adversary only has access to classical side information about the source.

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arXiv2025

Defining Security in Quantum Key Distribution

The security of quantum key distribution (QKD) is quantified by a parameter $\varepsilon>0$, which -- under well-defined physical assumptions -- can be bounded explicitly. This contrasts with computationally secure schemes, where security claims are only asymptotic (i.e., under standard complexity assumptions, one only knows that $\varepsilon \to 0$ as the key size grows, but has no explicit bound). Here we explain the definition and interpretation of $\varepsilon$-security. Adopting an axiomatic approach, we show that $\varepsilon$ can be understood as the maximum probability of a security failure. Finally, we review and address several criticisms of this definition that have appeared in the literature.

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arXiv2025

Improved Two-source Extractors against Quantum Side Information

Two-source extractors aim to extract randomness from two independent sources of weak randomness. It has been shown that any two-source extractor which is secure against classical side information remains secure against quantum side information. Unfortunately, this generic reduction comes with a significant penalty to the performance of the extractor. In this paper, we show that the two-source extractor from Dodis et al. performs equally well against quantum side information as in the classical realm, surpassing previously known results about this extractor. Additionally, we derive a new quantum XOR-Lemma which allows us to re-derive the generic reduction but also allows for improvements for a large class of extractors.

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arXiv2025

Cyclic quantum causal modelling with a graph separation theorem

Causal modelling frameworks link observable correlations to causal explanations, which is a crucial aspect of science. These models represent causal relationships through directed graphs, with vertices and edges denoting systems and transformations within a theory. Most studies focus on acyclic causal graphs, where well-defined probability rules and powerful graph-theoretic properties like the d-separation theorem apply. However, understanding complex feedback processes and exotic fundamental scenarios with causal loops requires cyclic causal models, where such results do not generally hold. While progress has been made in classical cyclic causal models, challenges remain in uniquely fixing probability distributions and identifying graph-separation properties applicable in general cyclic models. In cyclic quantum scenarios, existing frameworks have focussed on a subset of possible cyclic causal scenarios, with graph-separation properties yet unexplored. This work proposes a framework applicable to all consistent quantum and classical cyclic causal models on finite-dimensional systems. We address these challenges by introducing a robust probability rule and a novel graph-separation property, p-separation, which we prove to be sound and complete for all such models. Our approach maps cyclic causal models to acyclic ones with post-selection, leveraging the post-selected quantum teleportation protocol. We characterize these protocols and their success probabilities along the way. We also establish connections between this formalism and other classical and quantum frameworks to inform a more unified perspective on causality. This provides a foundation for more general cyclic causal discovery algorithms and to systematically extend open problems and techniques from acyclic informational networks (e.g., certification of non-classicality) to cyclic causal structures and networks.

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arXiv2025

Cyclic functional causal models beyond unique solvability with a graph separation theorem

Functional causal models (fCMs) specify functional dependencies between random variables associated to the vertices of a graph. In directed acyclic graphs (DAGs), fCMs are well-understood: a unique probability distribution on the random variables can be easily specified, and a crucial graph-separation result called the d-separation theorem allows one to characterize conditional independences between the variables. However, fCMs on cyclic graphs pose challenges due to the absence of a systematic way to assign a unique probability distribution to the fCM's variables, the failure of the d-separation theorem, and lack of a generalization of this theorem that is applicable to all consistent cyclic fCMs. In this work, we develop a causal modeling framework applicable to all cyclic fCMs involving finite-cardinality variables, except inconsistent ones admitting no solutions. Our probability rule assigns a unique distribution even to non-uniquely solvable cyclic fCMs and reduces to the known rule for uniquely solvable fCMs. We identify a class of fCMs, called averagely uniquely solvable, that we show to be the largest class where the probabilities admit a Markov factorization. Furthermore, we introduce a new graph-separation property, p-separation, and prove this to be sound and complete for all consistent finite-cardinality cyclic fCMs while recovering the d-separation theorem for DAGs. These results are obtained by considering classical post-selected teleportation protocols inspired by analogous protocols in quantum information theory. We discuss further avenues for exploration, linking in particular problems in cyclic fCMs and in quantum causality.

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