arXiv subjects

Mario Berta

Publications and source records attributed to Mario Berta.

At least 19 recordsLinked to original sources

arXiv2026

Second-Order Expansion of Privacy Amplification Under f-Divergence Criteria

We derive the second-order asymptotics of randomness extraction from memoryless sources with side information under security criteria based on a broad class of Csisz\`ar f-divergences, treating both a fixed reference side-information marginal and optimization over that marginal. The conditional varentropy decomposes into fluctuations of the conditional entropy across different values of the side information and the average variance of the conditional surprisal for each value. Without marginal optimization, these contributions yield a Gaussian-mixture second-order profile. With marginal optimization, they combine into the total conditional varentropy, yielding a single Gaussian profile. As corollaries, we obtain second-order expansions for R\'enyi-entropy criteria of all orders $\alpha \in (0,1)$ and recover the known expansion for total variation distance.

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arXiv2026

Constant-time equilibration of observables under rapid Lindbladian dynamics

Markovian open-system dynamics have widespread applications throughout quantum information science, including algorithmic state preparation. Their convergence is commonly quantified using the worst case global trace distance between the evolving and stationary states. However, this criterion can be unnecessarily stringent when only physically relevant observables are of interest. Here we introduce and study observable-specific mixing times. We prove that, for quasi-local, rapidly mixing Lindbladians, sums of geometrically local observables equilibrate in a time independent of system size, in contrast to the logarithmic dependence of global state mixing. This separation reduces the runtime of dissipative quantum algorithms, including quantum Gibbs samplers, for estimating quantities such as the Gibbs state energy and local order parameters, yielding an overall scaling that is linear in system size. Complementing this quantum result, we develop a quantum-inspired classical algorithm for estimating the same quantities. Its runtime is likewise linear in system size, but scaling exponentially in $\mathcal{O}\big(\log(1/\epsilon)^D\big)$, where $D$ denotes the spatial dimension of the lattice. We further analyse non-interacting Lindbladians over qudits, fermions, and bosons, demonstrating that locality of observables is not always necessary for a qualitatively faster mixing. Small-scale simulations of quantum Gibbs samplers reveal no large hidden constants in our asymptotic analysis and show that the theoretical predictions closely capture the finite-size dynamics.

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arXiv2026

Strong Converse Exponent of Quantum State Merging

We determine the strong converse exponent for the entanglement cost of quantum state merging, showing that it is characterized by the optimized $\alpha$-$z$ conditional R\'enyi entropies with $z=\alpha/2\in[1/2,1]$. This contrasts with the sandwiched conditional R\'enyi entropies that typically govern strong converse exponents in quantum information theory. As a consequence, we derive the strong converse exponent of the partially smoothed conditional min-entropy in purified distance. This exponent is governed by club-sandwiched conditional entropies, whereas global smoothing leads to a sandwiched expression.

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arXiv2026

Convergence monitoring of quantum Gibbs samplers

Recent progress in fully quantum Markov chain Monte Carlo methods enables efficient Gibbs-state sampling on quantum computers [Chen et al., Nature 646, 561 (2025)]. Although rigorous worst-case bounds on mixing times remain largely inaccessible for classically intractable systems, experience from classical Monte Carlo suggests that convergence of relevant observables may nevertheless be rapid. This raises the practical question of how to diagnose convergence efficiently, i.e., with at most polynomial overhead. We propose a low-cost criterion for convergence monitoring that exploits the weak measurements inherent in quantum Gibbs samplers and their qubit-efficient variants [Ding et al., arXiv:2508.05703 (2025)]. Our approach is based on the observation that, at thermal equilibrium, the net energy flow between system and environment vanishes and energy-exchange statistics satisfy a balance condition. This condition appears in the distribution of (quasi-)frequencies extracted from the weak-measurement record and we use it to construct a Hamiltonian-agnostic stopping criterion based solely on data already generated by the sampler. We provide a statistical analysis, along with numerical and analytical studies to understand its performance, assumptions, and limitations.

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arXiv2026

Sharp continuity of quantum conditional entropy

We prove the sharp uniform continuity bound for quantum conditional entropy. If two bipartite states are at trace distance at most $\delta$ and $d=\dim A$, the optimal dimension-only modulus of continuity is $h_2(\delta)+\delta\log(d^2-1)$ up to $\delta=1-d^{-2}$ and $2\log d$ thereafter, where $h_2$ denotes the binary entropy. When $\dim B\ge d$, this bound is tight for every $\delta\in[0,1]$. The key proof idea was developed with the assistance of ChatGPT 5.6 Sol, building on and adapting the tight classical proof of Alhejji \& Smith [IEEE ISIT (2020)], which follows a conceptually different approach.

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arXiv2026

Superadditivity for Entanglement-Assisted Communication

The entanglement-assisted capacity of a quantum channel admits an additive single-letter characterization, implying that joint encodings across channel uses cannot increase the ultimate communication rate. Here, we show that this additive picture does not extend to communication reliability. Specifically, we prove that the Petz-R\'enyi channel information can be strictly superadditive for every $\alpha\in[1/2,1)$, yielding a genuine multi-copy enhancement of the entanglement-assisted random-coding error exponent, even though the entanglement-assisted capacity remains additive. We establish this phenomenon analytically already for measurement channels, which are entanglement-breaking and have additive unassisted capacity. Remarkably, this strict superadditivity is witnessed by a separable, classically correlated two-copy channel-input marginal, demonstrating that no entanglement between the transmitted systems is required. Our results show that, although correlations across channel uses cannot increase the ultimate rate of entanglement-assisted communication, they can enhance its reliability.

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arXiv2026

Tight any-shot quantum decoupling

Quantum information decoupling is a fundamental primitive in quantum information theory, underlying various applications in quantum physics. We prove a novel one-shot decoupling theorem formulated in terms of quantum relative entropy distance, with the decoupling error bounded by two sandwiched R\'enyi conditional entropies. In the asymptotic i.i.d. setting of standard information decoupling via partial trace, we show that this bound is ensemble-tight in quantum relative entropy distance and thereby yields a characterization of the associated decoupling error exponent in the low-cost-rate regime. Leveraging this framework, we derive several operational applications formulated in terms of purified distance: (i) single-letter expressions for the exact error exponents of quantum state merging in the low-entanglement-cost and high-entanglement-distillation-rate regimes, in terms of Petz-R\'enyi conditional entropies, and (ii) regularized expressions for achievable error exponents of entanglement distillation and quantum channel coding in terms of Petz-R\'enyi coherent informations. We further prove that these achievable bounds are tight for maximally correlated states and generalized dephasing channels, respectively, for the high distillation-rate/coding-rate regimes.

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arXiv2025

Routed Bell tests with arbitrarily many local parties

Device-independent quantum key distribution (DIQKD) promises cryptographic security based solely on observed quantum correlations, yet its implementation over long distances remains limited. Routed Bell tests have recently re-emerged as a promising strategy to mitigate this limitation by enabling local self-testing of one party's device. However, extending this idea to self-testing both communicating parties has remained unclear. Here we develop a general $C^*$-algebraic for routed DIQKD with multiple switches and arbitrarily many local test parties, with a conservative, state-dependent definition of Eve. Within this framework, we design and analyse four-party routed protocols that locally self-test both Alice as well as Bob, and numerically bound key rates from the full observed statistics. In the parameter regimes considered, adding a fourth party strictly improves certified key rates and lowers the non-zero key threshold. Randomized key-basis switching further amplifies this advantage. Finally, we investigate a self-test-assisted E91-type protocol that continuously interpolates between the device-dependent Shor-Preskill rate and the device-independent rate derived by [Pironio et al., New J. Phys. 11, 045021 (2009)].

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arXiv2025

Fundamental Quality Bound on Optical Quantum Communication

Sending quantum information reliably over long distances is a central challenge in quantum technology in general, and in quantum optics in particular, since most quantum communication relies on optical fibres or free-space links. Here, we address this problem by shifting the focus from the quantity of information sent to the quality of the transmission, i.e. the rate of decay of the transmission error with respect to the number of channel uses. For the general class of teleportation-simulable channels, which includes all channels arising in quantum optical communication, we prove that the single-letter reverse relative entropy of entanglement of the Choi state upper bounds the error exponent of two-way assisted quantum communication - paralleling the celebrated capacity bound of [Pirandola et al., Nat. Comm. (2017)] in terms of the regularised relative entropy of entanglement. Remarkably, for Gaussian channels our bound can be computed efficiently through a convex program with simple constraints involving only finite-dimensional covariance matrices. As a prototypical application, we derive closed-form analytical expressions of our upper bound as well as random-coding-based lower bounds for several one-mode Gaussian channels. Extending recent work [Lami et al., arXiv:2408.07067 (2024)] to infinite-dimensional systems, we further endow the reverse relative entropy of entanglement with an exact operational interpretation in entanglement testing, and show that it characterises the rate of entanglement distillation under non-entangling operations. These findings offer a new perspective on entanglement as a resource and sharpen the theoretical benchmarks for future quantum optical networks.

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arXiv2025

Rapid Mixing of Quantum Gibbs Samplers for Weakly-Interacting Quantum Systems

Dissipative quantum algorithms for state preparation in many-body systems are increasingly recognised as promising candidates for achieving large quantum advantages in application-relevant tasks. Recent advances in algorithmic, detailed-balance Lindbladians enable the efficient simulation of open-system dynamics converging towards desired target states. However, the overall complexity of such schemes is governed by system-size dependent mixing times. In this work, we analyse algorithmic Lindbladians for Gibbs state preparation and prove that they exhibit rapid mixing, i.e., convergence in time poly-logarithmic in the system size. We first establish this for non-interacting spin systems, free fermions, and free bosons, and then show that these rapid mixing results are stable under perturbations, covering weakly interacting qudits and perturbed non-hopping fermions. Further, we adapt the techniques from separable qudits to the fermionic setting and prove rapid mixing of the strongly-interacting regime of the Fermi-Hubbard model, for which we also explicitly evaluate the guaranteed parameter regimes. Our results constitute the first efficient mixing bounds for non-commuting qudit models and bosonic systems at arbitrary temperatures. Compared to prior spectral-gap-based results for fermions, we achieve exponentially faster mixing, further featuring explicit constants on the maximal allowed interaction strength. This not only improves the overall polynomial runtime for quantum Gibbs state preparation, but also enhances robustness against noise. Our analysis relies on oscillator norm techniques from mathematical physics, where we introduce tailored variants adapted to specific Lindbladians $\unicode{x2014}$ an innovation that we expect to significantly broaden the scope of these methods.

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arXiv2025

Strong converse exponent of channel interconversion

In their seminal work, Bennett et al. [IEEE Trans. Inf. Theory (2002)] showed that, with sufficient shared randomness, one noisy channel can simulate another at a rate equal to the ratio of their capacities. We establish that when coding above this channel interconversion capacity, the exact strong converse exponent is characterized by a simple optimization involving the difference of the corresponding R\'enyi channel capacities with H\"older dual parameters. We further extend this result to the entanglement-assisted interconversion of classical-quantum channels, showing that the strong converse exponent is likewise determined by differences of sandwiched R\'enyi channel capacities. The converse bound is obtained by relaxing to non-signaling assisted codes and applying H\"older duality together with the data processing inequality for R\'enyi divergences. Achievability is proven by concatenating refined channel coding and simulation protocols that go beyond first-order capacities, attaining an exponentially small conversion error, remaining robust under small variations in the input distribution, and tolerating a sublinear gap between the conversion rates.

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arXiv2025

Approximating fixed size quantum correlations in polynomial time

We show that $\varepsilon$-additive approximations of the optimal value of fixed-size two-player free games with fixed-dimensional entanglement assistance can be computed in time $\mathrm{poly}(1/\varepsilon)$. This stands in contrast to previous analytic approaches, which focused on scaling with the number of questions and answers, but yielded only strict $\mathrm{exp}(1/\varepsilon)$ guarantees. Our main result is based on novel Bose-symmetric quantum de Finetti theorems tailored for constrained quantum separability problems. These results give rise to semidefinite programming (SDP) outer hierarchies for approximating the entangled value of such games. By employing representation-theoretic symmetry reduction techniques, we demonstrate that these SDPs can be formulated and solved with computational complexity $\mathrm{poly}(1/\varepsilon)$, thereby enabling efficient $\varepsilon$-additive approximations. In addition, we introduce a measurement-based rounding scheme that translates the resulting outer bounds into certifiably good inner sequences of entangled strategies. These strategies can, for instance, serve as warm starts for see-saw optimization methods. We believe that our techniques are of independent interest for broader classes of constrained separability problems in quantum information theory.

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arXiv2025

On approximate quantum error correction for symmetric noise

We revisit the extendability-based semi-definite programming hierarchy introduced by Berta et al. [Mathematical Programming, 1 - 49 (2021)], which provides converging outer bounds on the optimal fidelity of approximate quantum error correction (AQEC). As our first contribution, we introduce a measurement-based rounding scheme that extracts inner sequences of certifiably good encoder-decoder pairs from this outer hierarchy. To address the computational complexity of evaluating fixed levels of the hierarchy, we investigate the use of symmetry-based dimension reduction. In particular, we combine noise symmetries - such as those present in multiple copies of the qubit depolarizing channel - with the permutational symmetry arising from the extendability of the optimization variable. This framework is illustrated through basic, but already challenging numerical examples that showcase its practical effectiveness. Our results contribute to narrowing the gap between theoretical developments in quantum information theory and their practical applications in the analysis of small-scale quantum error-correcting codes.

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arXiv2025

Channel coding against quantum jammers via minimax

We introduce a minimax approach for characterizing the capacities of fully quantum arbitrarily varying channels (FQAVCs) under different shared resource models. In contrast to previous methods, our technique avoids de Finetti-type reductions, providing a more streamlined proof without dependency on the dimension of the jamming system. Consequently, we show that the entanglement-assisted and shared-randomness-assisted capacities of FQAVCs match those of the corresponding compound channels, even in the presence of general quantum adversaries.

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arXiv2025

Strong converse Exponents of Partially Smoothed Information Measures

Partially smoothed information measures are fundamental tools in one-shot quantum information theory. In this work, we determine the exact strong converse exponents of these measures for both pure quantum states and classical states. Notably, we find that the strong converse exponents based on trace distance takes different forms between pure and classical states, indicating that they are not uniform across all quantum states. Leveraging these findings, we derive the strong converse exponents for quantum data compression, intrinsic randomness extraction, and classical state splitting. A key technical step in our analysis is the determination of the strong converse exponent for classical privacy amplification, which is of independent interest.

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arXiv2025

Quantum umlaut information

We study the quantum umlaut information, a correlation measure defined for bipartite quantum states $\rho_{AB}$ as a reversed variant of the quantum mutual information: $U(A;B)_\rho = \min_{\sigma_B} D(\rho_A\otimes \sigma_B\|\rho_{AB})$ in terms of the quantum relative entropy $D$. As in the classical case [Girardi et al., arXiv:2503.18910], this definition allows for a closed-form expression and has an operational interpretation as the asymptotic error exponent in the hypothesis testing task of deciding whether a given bipartite state is product or not. We generalise the umlaut information to quantum channels, where it also extends the notion of `oveloh information' [Nuradha et al., arXiv:2404.16101]. We prove that channel umlaut information is additive for classical-quantum channels, while we observe additivity violations for fully quantum channels. Inspired by recent results in entanglement theory, we then show as our main result that the regularised umlaut information constitutes a fundamental measure of the quality of classical information transmission over a quantum channel -- as opposed to the capacity, which quantifies the quantity of information that can be sent. This interpretation applies to coding assisted by activated non-signalling correlations, and the channel umlaut information is in general larger than the corresponding expression for unassisted communication as obtained by Dalai for the classical-quantum case [IEEE Trans. Inf. Theory 59, 8027 (2013)]. Combined with prior works on non-signalling--assisted zero-error channel capacities, our findings imply a dichotomy between the settings of zero-rate error exponents and zero-error communication. While our results are single-letter only for classical-quantum channels, we also give a single-letter bound for fully quantum channels in terms of the `geometric' version of umlaut information.

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arXiv2025

Umlaut information

The sphere-packing bound quantifies the error exponent for noisy channel coding for rates above a critical value. Here, we study the zero-rate limit of the sphere-packing bound and show that it has an intriguing single-letter form, which we call the umlaut information of the channel, inspired by the lautum information introduced by Palomar and Verd\'u. Unlike the latter quantity, we show that the umlaut information is additive for parallel uses of channels. We show that it has a twofold operational interpretation: as the zero-rate error exponent of non-signalling-assisted coding on the one hand, and as the zero-rate error exponent of list decoding in the large list limit on the other.

cs.IT↗

arXiv2025

Quantum Entropy Prover

Information inequalities govern the ultimate limitations in information theory and as such play an pivotal role in characterizing what values the entropy of multipartite states can take. Proving an information inequality, however, quickly becomes arduous when the number of involved parties increases. For classical systems, [Yeung, IEEE Trans. Inf. Theory (1997)] proposed a framework to prove Shannon-type inequalities via linear programming. Here, we derive an analogous framework for quantum systems, based on the strong sub-additivity and weak monotonicity inequalities for the von-Neumann entropy. Importantly, this also allows us to handle constrained inequalities, which - in the classical case - served as a crucial tool in proving the existence of non-standard, so-called non-Shannon-type inequalities [Zhang & Yeung, IEEE Trans. Inf. Theory (1998)]. Our main contribution is the Python package qITIP, for which we present the theory and demonstrate its capabilities with several illustrative examples

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