arXiv subjects

Ludovico Lami

Publications and source records attributed to Ludovico Lami.

At least 19 recordsLinked to original sources

arXiv2026

Entropic measures of quantum information

Entropy has played a pivotal role in physics ever since its inception by Clausius in the early industrial age. Shannon ushered the concept into the information age by using it to describe fundamental limits of information processing, founding the field of information theory. Today, a fruitful interaction between information theory and physics is pushing our understanding of entropy forward. It has revealed, in particular, that no single notion of entropy suffices to capture all relevant properties of physical systems, making it necessary to consider a variety of entropic measures of quantum information, each with distinct features and uses. This review surveys these recent advances in a structured way, covering a comprehensive array of information measures, including Rényi and smooth entropies, together with their interrelations. Starting with a systematic characterization of entropies that motivates their definitions from natural physical principles, we discuss their applications ranging from quantum communication and cryptography to resource theories, thermodynamics, and many-body physics.

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arXiv2026

Principles of Quantum Communication Theory: A Modern Approach

This is a preliminary version of a book in progress on the theory of quantum communication. We adopt an information-theoretic perspective throughout and give a comprehensive account of fundamental results in quantum communication theory from the past decade (and earlier), with an emphasis on the modern one-shot-to-asymptotic approach that underlies much of today's state-of-the-art research in this field. In Part I, we cover mathematical preliminaries and provide a detailed study of quantum mechanics from an information-theoretic perspective. We also provide an extensive and thorough review of quantum entropies, and we devote an entire chapter to the study of entanglement measures. Equipped with these essential tools, in Part II we study classical communication (with and without entanglement assistance), entanglement distillation, quantum communication, secret key distillation, and private communication. In Part III, we cover the latest developments in feedback-assisted communication tasks, such as quantum and classical feedback-assisted communication, LOCC-assisted quantum communication, and secret key agreement.

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arXiv2026

Sample complexity of quantum resource testing via one-shot quantum blurring

Quantum resource testing is a fundamental primitive of quantum information processing, profoundly connected to resource manipulation. Its goal is to discriminate $n$ copies of a given resourceful state $ρ$ from all free (i.e., resourceless) states; key instances for applications are entanglement testing and quantum magic testing. The asymptotic characterisation relies on the recently proven Generalised Quantum Stein's Lemma (GQSL), which establishes the rate of decay of the false negative error probability for a fixed false positive error probability. This result, however, is intrinsically asymptotic and thus can provide no finite-resource guarantees, which makes its practical implications unclear. Here, we establish the first rigorous finite-$n$ bounds on quantum resource testing and hence quantum resource manipulation, thus strengthening the GQSL and providing explicit estimates on the number of copies needed to achieve a prescribed performance. As notable consequences, we obtain (a) the convergence of the regularised Rényi relative entropies of a resource, which settles the important open problem from [Fang/Hayashi, arXiv:2508.12901, IEEE ToIT 72:6, 2026]; and (b) the first sample-complexity bound for asymmetric resource testing: for any fixed false positive error probability, a false negative error probability of at most $δ$ can be achieved with $n=O\left(\frac{\log(1/δ)}{D^\infty(ρ\|\mathcal F)}\right)$ copies of $ρ$, in the limit where $δ\to 0$.

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arXiv2026

Universal quantum coding

Entanglement distillation from noisy bipartite states and reliable quantum communication over noisy channels are fundamental tasks in quantum information theory. Yet existing coding schemes typically require prior knowledge of the underlying state or channel, or assume independent or weakly correlated quantum information sources. Here, using Schur-Weyl duality, we establish a universal quantum error-correction principle that overcomes these limitations. We show that the irreducible permutation spaces arising from the local Schur-Weyl decomposition of multiple copies of an unknown bipartite mixed state form maximally entangled quantum code spaces whose error structure is governed entirely by representation theory. Correcting these symmetry-resolved errors yields protocols for entanglement distillation and quantum communication that achieve coherent-information rates with exponentially vanishing error and optimal second-order corrections, even in the case of almost i.i.d. resources. Our approach also provides sharp finite-copy guarantees that are worst-case optimal at every finite block length, including in the sample-efficient regime, where the number of copies scales only polynomially with the number of qubits. Together, these results establish Schur-Weyl duality as a general mechanism for universal, robust, and optimal quantum coding, unifying entanglement distillation, quantum error correction, and quantum communication within a common representation-theoretic framework.

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arXiv2026

Classical Capacity of Single-Mode Bosonic Gaussian Channels

The classical capacity of a noisy optical channel is the maximum rate at which information can be transmitted reliably, given a constraint on the mean input energy. For the ubiquitous bosonic Gaussian channels, which include standard models of loss and noise in fibre and free-space optical links, determining this rate requires addressing whether entanglement between channel uses or non-Gaussian signals can outperform Gaussian encodings. More precisely, the question is whether the energy-constrained Holevo information is additive across arbitrarily many channel uses and coincides with its Gaussian counterpart. We answer these fundamental questions in the affirmative for every single-mode bosonic Gaussian channel at every input energy. Namely, we prove that independently prepared Gaussian states with Gaussian-distributed random displacements achieve the capacity, including in the low-energy regime where squeezing the signals competes with encoding information in their displacement. Our proof connects an entanglement inequality to a sharp, additive lower bound on output entropy. We then characterise communication above capacity: under a strict total photon-number cutoff, the probability of correct decoding decreases exponentially with the number of channel uses, and we derive explicit bounds on the decay exponent. When only the mean photon number is constrained, a simple energy-rescaling formula determines exactly the entire asymptotic rate--error trade-off: the capacity at mean photon number $N$ and allowed average decoding error $ε$ equals the vanishing-error capacity at mean photon number $N/(1-ε)$. Together, these results identify the ultimate limits of classical communication for some of the most fundamental models of optical communication.

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arXiv2026

Energy-constrained two-way capacities of the pure-loss channel

We determine the two-way quantum and secret-key capacities of the pure-loss channel under an average input photon-number constraint. For transmissivity $η$ and photon budget $N$, both capacities equal $g(N)-g((1-η)N)$, where $g$ is the entropy of a thermal state. This coincides with the rate achieved by the known reverse coherent information of a two-mode squeezed vacuum. Our result provides the last missing capacity formula for the celebrated pure-loss channel, completing the picture of bosonic quantum communication under pure loss.

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arXiv2026

On PPT entanglement distillation

We study entanglement distillation under operations that remain completely positive under partial-transpose conjugation, a.k.a. PPT channels, in the standard quantum Shannon theory regime of asymptotically vanishing but non-zero error. Our main results are: (a) a regularised formula for the PPT distillable entanglement in terms of a measured-relative-entropy-like quantity; and (b) two different single-letter converses, one based on operator quadratic forms and the other on Hirschman's strengthening of the Hadamard three-line theorem. As an immediate application of (b), we show that the PPT distillable entanglement can be strictly smaller than the regularised Rains bound, thereby resolving an open problem in the theory of entanglement manipulation [Regula et al., NJP 21:103017, 2019]. A gap appears already for $3\times 3$ Werner states: at antisymmetric weight $25/26$, a certified upper bound of $0.62107$ ebits lies below the (regularised) Rains bound, which equals $\frac{25}{26} \log_2 5 - \log_2 3 \approx 0.64766$ ebits. On a different note, (a) implies a faithful lower bound on the PPT distillable entanglement in terms of the entanglement negativity, which provides a quantitative counterpart to the qualitatively known fact that any NPT state is PPT distillable [Eggeling et al., PRL 87:257902, 2001].

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arXiv2026

Quantum information processing under maximal distance measures

The measures of distance frequently used in quantum information, such as trace distance or fidelity-based purified distance, are the smallest extensions of the corresponding distance measures in classical information theory. However, this way of extending classical distances is not unique, and a whole spectrum of other extensions can be defined. Here we study the question of how quantum information processing tasks are affected by a change of the error metrics to the maximal extensions of the classical distance measures, imposing more demanding error requirements on operational tasks. We find that the performance of some tasks, such as channel coding or quantum resource distillation, is not affected whatsoever by this change. However, for other tasks such as channel simulation and quantum resource dilution, we show that the rates are now given not by functions of the standard (Umegaki) quantum relative entropy, but ones based on the Belavkin-Staszewski relative entropy. Our results connect the Belavkin-Staszewski relative entropy with operational tasks and reveal that known reversibility results in quantum information, including the reverse Shannon theorem and the asymptotic reversibility of quantum resource transformations, no longer hold under maximal distance measures.

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arXiv2026

Discriminating Lindbladian Dynamics

The fundamental task of quantum hypothesis testing, which consists in discriminating quantum objects, has been extensively studied for quantum states and channels. Here, we investigate the fundamental limits of discriminating an arbitrary pair of quantum Markovian dynamics generated by Lindbladians, focusing on the roles of total exposure time and temporal resolution. We allow adaptive choices of evolution durations and arbitrary instantaneous controls between them. We characterise the optimal type-II error exponent (Stein exponent) as the largest instantaneous increase of quantum relative entropy, and give an algebraic criterion for its finiteness in terms of the Lindbladians. Remarkably, an infinite exponent is equivalent to a vanishing type-II error probability at sufficiently large finite total time, for every positive type-I tolerance. While some dynamics admit a finite protocol with zero type-II error, others require increasingly fine temporal control. For the latter, the error vanishes as the minimum allowed evolution duration, or resolution time, tends to zero at fixed sufficiently large total time, but remains bounded away from zero at every fixed positive resolution time. We achieve this using quantum Zeno protocols, establishing temporal resolution as a resource for discrimination. When the null hypothesis is the identity semigroup, an infinite asymptotic error exponent has a stronger consequence: at a fixed finite total exposure time, the type-II error can be made arbitrarily small while keeping the type-I error exactly zero. This is impossible in the corresponding classical setting. Discriminating the identity semigroup from generalised amplitude damping on a qubit provides examples of all three regimes: a finite asymptotic error exponent, zero type-II error attainable at positive resolution time, and vanishing type-II error requiring the resolution time to tend to zero.

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arXiv2026

Universal Entanglement Distillation

We present a universal entanglement distillation protocol that asymptotically achieves the distillable entanglement of any unknown bipartite state in a fixed finite dimension. That is, its ebit yield attains every rate below the optimum that would be available if the state were known, with vanishing trace-distance error. Our approach combines tomography by local operations and classical communication with an adaptive distillation routine, using a local robustness lemma to control finite-sample estimation errors. We also characterize worst-case distillation from a family of states: the optimal uniform rate is the minimum distillable entanglement on the family's closure. These results show that ignorance of the state need not incur an asymptotic rate penalty.

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arXiv2026

A fully Gaussian quantum Stein's lemma

A central yet mysterious problem in quantum information is the asymptotic distinguishability of quantum states under restricted measurements. Here we look at asymptotic asymmetric hypothesis testing for general multi-mode bosonic Gaussian states restricted to arbitrary collective Gaussian measurements. We establish a single-letter formula for the Stein exponent for many pairs of states, featuring two distinct contributions, corresponding to first and second moments, respectively. Remarkably, the Gaussian-measured relative entropy exhibits genuine non-additivity, but the only effect of additivity violations is to asymptotically decouple first and second moments. We prove this by establishing sufficient conditions for additivity of the second-moment term via novel log-determinant matrix inequalities. Our results not only identify a single-letter expression for the Gaussian Stein exponent in a wide range of practical situations, but also rule out any possible advantage from collective Gaussian measurements when considering centred Gaussian states.

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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 $δ$ and $d=\dim A$, the optimal dimension-only modulus of continuity is $h_2(δ)+δ\log(d^2-1)$ up to $δ=1-d^{-2}$ and $2\log d$ thereafter, where $h_2$ denotes the binary entropy. When $\dim B\ge d$, this bound is tight for every $δ\in[0,1]$. 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

Optimal Discrimination of Gaussian States by Gaussian Measurements

Are Gaussian measurements enough to distinguish between Gaussian states? Here, we tackle this question by focusing on the max-relative entropy as an operational distinguishability metric. Given two general multimode Gaussian states, we derive a condition, based on their covariance matrices, that completely determines whether or not there exists an optimal Gaussian measurement achieving the max-relative entropy. When the condition is satisfied, we find this optimal measurement explicitly. When the condition is not met, there is a strict gap between the distinguishability achievable by Gaussian measurements and the unconstrained max-relative entropy in which all measurements are allowed. We illustrate our results in the single-mode setting, and show examples of states for which this gap can be made arbitrarily large, revealing novel instances of Gaussian data hiding.

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arXiv2026

Sharp pairwise reduction for quantum hypothesis testing

We determine the optimal universal coefficient in a reduction of multiple to binary quantum hypothesis testing. Specifically, for every finite ensemble in any Hilbert space dimension (finite or infinite), we prove that the error probability of the global pretty good measurement (PGM) is at most four times the sum of the optimal binary error probabilities. By constructing a family of regular-simplex ensembles, we further show that the coefficient four is optimal, even for arbitrary global measurements. This result improves on the pairwise bounds established by Cheng and Liu [arXiv:2606.06246 (2026)] and entails an explicit, sharp guarantee for the standard PGM itself. Our proof is also simpler: rather than constructing sequential measurements and applying a union bound, our proof relies on purely matrix-analytic techniques, combining a direct block Gram matrix analysis of the PGM error and a refined inequality between quantum Hellinger distance and Bures $χ^2$-divergence. Our analysis also yields a refined, one-shot pairwise Chernoff bound and explicit sufficient number of copies for a desired discrimination error.

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arXiv2026

Efficiently Computable Strategies and Limits for Bosonic Channel Discrimination

Discriminating between noisy quantum processes is a central primitive for quantum communication, metrology, and computing. While discrimination limits for finite-dimensional channels are well understood, the continuous-variable setting, particularly under experimentally relevant energy constraints, remains significantly less developed. In this work, we establish an energy-constrained chain rule for the Belavkin-Staszewski channel divergence, which yields a fundamental upper bound on the error exponents achievable by fully adaptive, energy-constrained quantum channel discrimination protocols. We then derive efficiently computable bounds on asymmetric error exponents for energy-constrained discrimination of bosonic dephasing and loss-dephasing channels. Specifically, we show that three operationally relevant quantities -- the measured relative entropy, the Umegaki relative entropy, and the geometric Renyi divergence -- admit semidefinite program (SDP) formulations when the input energy is bounded and the Hilbert space is suitably truncated. Applying these tools, we demonstrate that optimal probes for these channels under energy constraints are Fock-diagonal, and we also enable numerically precise evaluation of bounds on achievable error exponents across discrimination strategies ranging from separable to fully adaptive. The resulting SDPs provide practical benchmarks for quantum-limited sensing in low-energy bosonic platforms.

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arXiv2026

Generalised quantum Stein's lemma more robust than ever

The generalised quantum Stein's lemma is a key result in quantum hypothesis testing, and connects this fundamental primitive of quantum information processing with quantum resource manipulation, a task that is central for technological applications. Prior works have proved this statement in the idealised setting of independent and identically distributed (i.i.d.) sequences of quantum states, and recent extensions consider also sources that are 'close' to i.i.d., according to the strict notion put forth by Mazzola, Sutter, and Renner. For several applications, however, one would need to consider yet more general sources. We establish a version of the generalised quantum Stein's lemma that is conceptually much simpler and general, as it applies to any source that is asymptotically close to an i.i.d. state with respect to the normalised quantum Wasserstein distance of order 1. As an immediate consequence, we solve the Stein exponent of a scenario where the null hypothesis is arbitrarily varying, expressing it in terms of i.i.d. Stein exponents corresponding to arbitrary states in the convex hull of the null hypothesis base set.

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arXiv2026

New approaches to almost i.i.d. information theory

Independent and identically distributed (i.i.d.) states are ubiquitous in quantum information theory. However, in a practical setting, the i.i.d. assumption is too stringent, and possibly not realistic. A physically more compelling class of 'almost i.i.d.' sources was recently proposed by [Mazzola/Sutter/Renner, arXiv:2603.15792]. In this paper, we introduce two alternative definitions of almost i.i.d. states, based on the normalised quantum Wasserstein distance and on the idea of looking at the average $k$-body marginal. We explore some basic properties of these notions and prove a strict hierarchical relation among them, with Mazzola et al.'s notion being the strictest, the one based on $k$-body marginals the loosest, and the one based on the quantum Wasserstein distance in between. Strict separation is established by means of explicit examples.

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arXiv2026

Entanglement of flower states

The mysterious nature of entanglement, one of the most prominent exquisitely quantum phenomena, is reflected in its intricate operational structure, with a hierarchy of classes of free operations that enable its manipulation at different levels of effectiveness. Here we use the class of 'flower states', parametrised by their (even) local dimension $2k$, to shine light on some aspects of this varied landscape. We compute all the main entanglement measures for flower states, uncovering a large gap between all forms of distillable entanglement, equal to 1 ebit independently of the local dimension, and the entanglement cost under local operations and classical communication (LOCC), known to be equal to $\log\big(2\sqrt{k}\big)$. Even under the strictly more powerful class of non-entangling (NE) operations, we show that their cost is still equal to $\log\big(1+\sqrt{k}\big)$, only about an ebit less than for LOCCs. This result, which we prove by calculating the recently introduced tempered entanglement negativity for these states, demonstrates the largest known 'irreversibility gap', i.e. the difference between distillable entanglement and entanglement cost, under NE operations, equal to $Θ\big(\frac12 \log d\big)$, with $d$ being the local dimension. A notable consequence is that the celebrated squashed entanglement is not a monotone under NE operations. Finally, we compute the exact cost under LOCC operations for flower states; this is given by the Schmidt number, which turns out to be additive over multiple copies and equal to $\min_{r|k} \log\left( r + \frac{k}{r} \right)$; for prime $k$ this reduces to $\log(k+1)$, about twice the standard LOCC cost. These last results leverage the uncertainty relations over cyclic groups proved by Tao and Meshulam.

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