arXiv subjects

Giulia Mazzola

Publications and source records attributed to Giulia Mazzola.

5 recordsLinked to original sources

arXiv2026

Robust generalized quantum Stein's lemma

The generalized quantum Stein's lemma provides an explicit expression for the optimal error exponent when distinguishing many independent and identically distributed (iid) copies of a given bipartite state from the set of separable bipartite states. Here we prove that this result is robust, in the sense that the iid assumption can be relaxed to almost-iid. In particular, our result shows that the original argument of Brand\~ao and Plenio, which contains a logical gap, can be made rigorous. Our proof relies on a novel continuity bound for the relative entropy of entanglement with respect to the quantum Wasserstein distance. Combined with a recent insight that almost-iid states and their exact iid counterparts are asymptotically close in this distance, the bound implies that their relative entropies of entanglement coincide asymptotically.

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arXiv2026

Almost-iid information theory

Information-theoretic techniques are based on the assumption that resources are well characterized by independent and identically distributed (iid) states. This assumption cannot be justified operationally, since, for example, correlations between subsequent systems emitted by a source cannot be detected by any practical tomographic protocol. Operationally motivated symmetry assumptions still imply, via de Finetti theorems, that the resources are described by almost-iid states. This raises the question: Are almost-iid resources as effective as perfect iid resources for information-processing tasks? Here we address this question and prove that the conditional entropy of almost-iid states asymptotically coincides with that of iid states. As an application, this implies that squashed entanglement is robust for almost-iid states, asymptotically matching its value on iid states.

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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

Uhlmann's theorem for relative entropies

Uhlmann's theorem states that, for any two quantum states $\rho_{AB}$ and $\sigma_A$, there exists an extension $\sigma_{AB}$ of $\sigma_A$ such that the fidelity between $\rho_{AB}$ and $\sigma_{AB}$ equals the fidelity between their reduced states $\rho_A$ and $\sigma_A$. In this work, we generalize Uhlmann's theorem to $\alpha$-R\'enyi relative entropies for $\alpha \in [\frac{1}{2},\infty]$, a family of divergences that encompasses fidelity, relative entropy, and max-relative entropy corresponding to $\alpha=\frac{1}{2}$, $\alpha=1$, and $\alpha=\infty$, respectively.

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arXiv2022

Gauge invariant quantum circuits for $U(1)$ and Yang-Mills lattice gauge theories

Quantum computation represents an emerging framework to solve lattice gauge theories (LGT) with arbitrary gauge groups, a general and long-standing problem in computational physics. While quantum computers may encode LGT using only polynomially increasing resources, a major openissue concerns the violation of gauge-invariance during the dynamics and the search for groundstates. Here, we propose a new class of parametrized quantum circuits that can represent states belonging only to the physical sector of the total Hilbert space. This class of circuits is compact yet flexible enough to be used as a variational ansatz to study ground state properties, as well as representing states originating from a real-time dynamics. Concerning the first application, the structure of the wavefunction ansatz guarantees the preservation of physical constraints such as the Gauss law along the entire optimization process, enabling reliable variational calculations. As for the second application, this class of quantum circuits can be used in combination with timedependent variational quantum algorithms, thus drastically reducing the resource requirements to access dynamical properties.

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