Publications (97)
The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
Mario Berta, Matthias Christandl, Renato Renner
The Quantum Reverse Shannon Theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to…
Asymptotic quantification of entanglement with a single copy
Ludovico Lami, Mario Berta, Bartosz Regula
Despite the central importance of quantum entanglement in quantum technologies, the understanding of the optimal ways to exploit it is still beyond our reach, and even measuring en…
Locally-Measured Rényi Divergences
Tobias Rippchen, Sreejith Sreekumar, Mario Berta
We propose an extension of the classical Rényi divergences to quantum states through an optimization over probability distributions induced by restricted sets of measurements. In…
A minimax approach to one-shot entropy inequalities
Anurag Anshu, Mario Berta, Rahul Jain +1
One-shot information theory entertains a plethora of entropic quantities, such as the smooth max-divergence, hypothesis testing divergence and information spectrum divergence, that…
Converse bounds for private communication over quantum channels
Mark M. Wilde, Marco Tomamichel, Mario Berta
This paper establishes several converse bounds on the private transmission capabilities of a quantum channel. The main conceptual development builds firmly on the notion of a priva…
Semidefinite programming hierarchies for constrained bilinear optimization
Mario Berta, Francesco Borderi, Omar Fawzi +1
We give asymptotically converging semidefinite programming hierarchies of outer bounds on bilinear programs of the form , maximized with respect…
Conditional Decoupling of Quantum Information
Mario Berta, Fernando G. S. L. Brandao, Christian Majenz +1
Insights from quantum information theory show that correlation measures based on quantum entropy are fundamental tools that reveal the entanglement structure of multipartite states…
On Variational Expressions for Quantum Relative Entropies
Mario Berta, Omar Fawzi, Marco Tomamichel
Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistic…
Quantum umlaut information
Filippo Girardi, Aadil Oufkir, Bartosz Regula +3
We study the quantum umlaut information, a correlation measure defined for bipartite quantum states as a reversed variant of the quantum mutual information: $U(A;B)_Ï= \…
Quasi-polynomial time algorithms for free quantum games in bounded dimension
Hyejung H. Jee, Carlo Sparaciari, Omar Fawzi +1
We give a converging semidefinite programming hierarchy of outer approximations for the set of quantum correlations of fixed dimension and derive analytical bounds on the convergen…
An equality between entanglement and uncertainty
Mario Berta, Patrick J. Coles, Stephanie Wehner
Heisenberg's uncertainty principle implies that if one party (Alice) prepares a system and randomly measures one of two incompatible observables, then another party (Bob) cannot pe…
Sharp continuity of quantum conditional entropy
Mario Berta, Pablo Costa Rico, Gereon Kossmann +2
We prove the sharp uniform continuity bound for quantum conditional entropy. If two bipartite states are at trace distance at most and , the optimal dimension-only m…
Rényi generalizations of quantum information measures
Mario Berta, Kaushik P. Seshadreesan, Mark M. Wilde
Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the Ré…
Identifying the Information Gain of a Quantum Measurement
Mario Berta, Joseph M. Renes, Mark M. Wilde
We show that quantum-to-classical channels, i.e., quantum measurements, can be asymptotically simulated by an amount of classical communication equal to the quantum mutual informat…
Amortization does not enhance the max-Rains information of a quantum channel
Mario Berta, Mark M. Wilde
Given an entanglement measure , the entanglement of a quantum channel is defined as the largest amount of entanglement that can be generated from the channel, if the sender…
Routed Bell tests with arbitrarily many local parties
Gereon KoÃmann, Mario Berta, René Schwonnek
Device-independent quantum key distribution (DIQKD) promises cryptographic security based solely on observed quantum correlations, yet its implementation over long distances remain…
Quantum algorithms: A survey of applications and end-to-end complexities
Alexander M. Dalzell, Sam McArdle, Mario Berta +10
The anticipated applications of quantum computers span across science and industry, ranging from quantum chemistry and many-body physics to optimization, finance, and machine learn…
Monotonicity of quantum relative entropy and recoverability
Mario Berta, Marius Lemm, Mark M. Wilde
The relative entropy is a principal measure of distinguishability in quantum information theory, with its most important property being that it is non-increasing with respect to no…
Catalytic Decoupling of Quantum Information
Christian Majenz, Mario Berta, Frédéric Dupuis +2
The decoupling technique is a fundamental tool in quantum information theory with applications ranging from quantum thermodynamics to quantum many body physics to the study of blac…
Single-shot Quantum State Merging
Mario Berta
We consider an unknown quantum state shared between two parties, Alice and Bob, and ask how much quantum communication is needed to transfer the full state to Bob. This problem is…
Quantum Resources Required to Block-Encode a Matrix of Classical Data
B. David Clader, Alexander M. Dalzell, Nikitas Stamatopoulos +3
We provide modular circuit-level implementations and resource estimates for several methods of block-encoding a dense matrix of classical data to precision ; the mi…
Quantum Channel Simulation and the Channel's Smooth Max-Information
Kun Fang, Xin Wang, Marco Tomamichel +1
We study the general framework of quantum channel simulation, that is, the ability of a quantum channel to simulate another one using different classes of codes. First, we show tha…
Disentanglement Cost of Quantum States
Mario Berta, Christian Majenz
We show that the minimal rate of noise needed to catalytically erase the entanglement in a bipartite quantum state is given by the regularized relative entropy of entanglement. Thi…
Approximating fixed size quantum correlations in polynomial time
Julius A. Zeiss, Gereon KoÃmann, Gereon Koßmann +2
We show that -additive approximations of the optimal value of fixed-size two-player free games with fixed-dimensional entanglement assistance can be computed in time $…
Computing Quantum Channel Capacities
Navneeth Ramakrishnan, Raban Iten, Volkher B. Scholz +1
The capacity of noisy quantum channels characterizes the highest rate at which information can be reliably transmitted and it is therefore of practical as well as fundamental impor…
Practical randomness amplification and privatisation with implementations on quantum computers
Cameron Foreman, Sherilyn Wright, Alec Edgington +2
We present an end-to-end and practical randomness amplification and privatisation protocol based on Bell tests. This allows the building of device-independent random number generat…
Deconstruction and conditional erasure of quantum correlations
Mario Berta, Fernando G. S. L. Brandao, Christian Majenz +1
We define the deconstruction cost of a tripartite quantum state on systems as the minimum rate of noise needed to apply to the systems, such that there is negligible dis…
Quantum Broadcast Channel Simulation via Multipartite Convex Splitting
Hao-Chung Cheng, Li Gao, Mario Berta
We show that the communication cost of quantum broadcast channel simulation under free entanglement assistance between the sender and the receivers is asymptotically characterized…
One-shot Multiple Access Channel Simulation
Aditya Nema, Sreejith Sreekumar, Mario Berta
We consider the problem of shared randomness-assisted multiple access channel (MAC) simulation for product inputs and characterize the one-shot communication cost region via almost…
Calculating response functions of coupled oscillators using quantum phase estimation
Sven Danz, Mario Berta, Stefan Schröder +3
We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these respons…
Strong Converse Exponent of Quantum Dichotomies
Mario Berta, Yongsheng Yao
The quantum dichotomies problem asks at what rate one pair of quantum states can be approximately mapped into another pair of quantum states. In the many copy limit and for vanishi…
Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
Mark M. Wilde, Mario Berta, Christoph Hirche +1
It is well known that for the discrimination of classical and quantum channels in the finite, non-asymptotic regime, adaptive strategies can give an advantage over non-adaptive str…
Smooth Entropy Bounds on One-Shot Quantum State Redistribution
Mario Berta, Matthias Christandl, Dave Touchette
In quantum state redistribution as introduced in [Luo and Devetak (2009)] and [Devetak and Yard (2008)], there are four systems of interest: the system held by Alice, the s…
Entanglement Cost of Quantum Channels
Mario Berta, Fernando Brandao, Matthias Christandl +1
The entanglement cost of a quantum channel is the minimal rate at which entanglement (between sender and receiver) is needed in order to simulate many copies of a quantum channel i…
The Uncertainty Principle in the Presence of Quantum Memory
Mario Berta, Matthias Christandl, Roger Colbeck +2
The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertaint…
Exponents for classical-quantum channel simulation in purified distance
Aadil Oufkir, Yongsheng Yao, Mario Berta
We determine the exact error and strong converse exponent for entanglement-assisted classical-quantum channel simulation in worst case input purified distance. The error exponent i…
A streamlined quantum algorithm for topological data analysis with exponentially fewer qubits
Sam McArdle, András Gilyén, Mario Berta
Topological invariants of a dataset, such as the number of holes that survive from one length scale to another (persistent Betti numbers) can be used to analyze and classify data i…
Tight any-shot quantum decoupling
Mario Berta, Hao-Chung Cheng, Yongsheng Yao
Quantum information decoupling is a fundamental primitive in quantum information theory, underlying various applications in quantum physics. We prove a novel one-shot decoupling th…
Quantum-proof randomness extractors via operator space theory
Mario Berta, Omar Fawzi, Volkher B. Scholz
Quantum-proof randomness extractors are an important building block for classical and quantum cryptography as well as device independent randomness amplification and expansion. Fur…
Renyi generalizations of the conditional quantum mutual information
Mario Berta, Kaushik P. Seshadreesan, Mark M. Wilde
The conditional quantum mutual information of a tripartite state is an information quantity which lies at the center of many problems in quantum information t…
Rényi squashed entanglement, discord, and relative entropy differences
Kaushik P. Seshadreesan, Mario Berta, Mark M. Wilde
In [Berta et al., J. Math. Phys. 56, 022205 (2015)], we recently proposed Renyi generalizations of the conditional quantum mutual information of a tripartite state on (with $…
Quantum Bilinear Optimization
Mario Berta, Omar Fawzi, Volkher B. Scholz
We study optimization programs given by a bilinear form over non-commutative variables subject to linear inequalities. Problems of this form include the entangled value of two-prov…
Quantum Coding with Finite Resources
Marco Tomamichel, Mario Berta, Joseph M. Renes
The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determin…
On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources
Mario Berta, Fernando G. S. L. Brandão, Gilad Gour +4
We show that the proof of the generalised quantum Stein's lemma [Brandão & Plenio, Commun. Math. Phys. 295, 791 (2010)] is not correct due to a gap in the argument leading to Lemm…
A Third Information-Theoretic Approach to Finite de Finetti Theorems
Mario Berta, Lampros Gavalakis, Ioannis Kontoyiannis
A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first random variables in an excha…
Gaussian hypothesis testing and quantum illumination
Mark M. Wilde, Marco Tomamichel, Seth Lloyd +1
Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, w…
Partially smoothed information measures
Anurag Anshu, Mario Berta, Rahul Jain +1
Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the su…
On Composite Quantum Hypothesis Testing
Mario Berta, Fernando G. S. L. Brandao, Christoph Hirche
We extend quantum Stein's lemma in asymmetric quantum hypothesis testing to composite null and alternative hypotheses. As our main result, we show that the asymptotic error exponen…
The Fidelity of Recovery is Multiplicative
Mario Berta, Marco Tomamichel
Fawzi and Renner [Commun. Math. Phys. 340(2):575, 2015] recently established a lower bound on the conditional quantum mutual information (CQMI) of tripartite quantum states i…
Entropic uncertainty and measurement reversibility
Mario Berta, Stephanie Wehner, Mark M. Wilde
The entropic uncertainty relation with quantum side information (EUR-QSI) from [Berta et al., Nat. Phys. 6, 659 (2010)] is a unifying principle relating two distinctive features of…
Quantum Side Information: Uncertainty Relations, Extractors, Channel Simulations
Mario Berta
In the first part of this thesis, we discuss the algebraic approach to classical and quantum physics and develop information theoretic concepts within this setup. In the second par…
Thermodynamic Implementations of Quantum Processes
Philippe Faist, Mario Berta, Fernando G. S. L. Brandao
Recent understanding of the thermodynamics of small-scale systems have enabled the characterization of the thermodynamic requirements of implementing quantum processes for fixed in…
Error exponent of activated non-signaling assisted classical-quantum channel coding
Aadil Oufkir, Marco Tomamichel, Mario Berta
We provide a tight asymptotic characterization of the error exponent for classical-quantum channel coding assisted by activated non-signaling correlations. Namely, we find that the…
Polynomial Time Quantum Gibbs Sampling for Fermi-Hubbard Model at any Temperature
Å tÄpán Å mÃd, Richard Meister, Mario Berta +1
Recently, there have been several advancements in quantum algorithms for Gibbs sampling. These algorithms simulate the dynamics generated by an artificial Lindbladian, which is met…
Strong converse Exponents of Partially Smoothed Information Measures
Mario Berta, Yongsheng Yao
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 measur…
A randomized quantum algorithm for statistical phase estimation
Kianna Wan, Mario Berta, Earl T. Campbell
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distincti…
One-shot decoupling
Frédéric Dupuis, Mario Berta, Jürg Wullschleger +1
If a quantum system A, which is initially correlated to another system, E, undergoes an evolution separated from E, then the correlation to E generally decreases. Here, we study th…
Strong converse exponent of channel interconversion
Aadil Oufkir, Yongsheng Yao, Mario Berta
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…
On approximate quantum error correction for symmetric noise
Gereon KoÃmann, Julius A. Zeiss, Omar Fawzi +1
We revisit the extendability-based semi-definite programming hierarchy introduced by Berta et al. [Mathematical Programming, 1 - 49 (2021)], which provides converging outer bounds…
Entanglement-assisted capacities of compound quantum channels
Mario Berta, Hrant Gharibyan, Michael Walter
We study universal quantum codes for entanglement-assisted quantum communication over compound quantum channels. In this setting, sender and receiver do not know the specific chann…
Quantum channel coding: Approximation algorithms and strong converse exponents
Aadil Oufkir, Mario Berta
We study relaxations of entanglement-assisted quantum channel coding and establish that non-signaling assistance and a natural semi-definite programming relaxation\, -- \,termed me…
Relating different quantum generalizations of the conditional Renyi entropy
Marco Tomamichel, Mario Berta, Masahito Hayashi
Recently a new quantum generalization of the Renyi divergence and the corresponding conditional Renyi entropies was proposed. Here we report on a surprising relation between condit…
Rényi divergences as weighted non-commutative vector valued -spaces
Mario Berta, Volkher B. Scholz, Marco Tomamichel
We show that Araki and Masuda's weighted non-commutative vector valued -spaces [Araki \& Masuda, Publ. Res. Inst. Math. Sci., 18:339 (1982)] correspond to an algebraic general…
Continuous Variable Quantum Key Distribution: Finite-Key Analysis of Composable Security against Coherent Attacks
Fabian Furrer, Torsten Franz, Mario Berta +4
We provide a security analysis for continuous variable quantum key distribution protocols based on the transmission of squeezed vacuum states measured via homodyne detection. We em…
Fundamental Quality Bound on Optical Quantum Communication
Tobias Rippchen, Ludovico Lami, Gerardo Adesso +1
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 communicat…
Qubit-Efficient Randomized Quantum Algorithms for Linear Algebra
Samson Wang, Sam McArdle, Mario Berta
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access t…
Limit Distribution Theory for Quantum Divergences
Sreejith Sreekumar, Mario Berta
Estimation of quantum relative entropy and its Rényi generalizations is a fundamental statistical task in quantum information theory, physics, and beyond. While several estimators…
Continuity of entropies via integral representations
Mario Berta, Ludovico Lami, Marco Tomamichel
We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main g…
Entanglement monogamy via multivariate trace inequalities
Mario Berta, Marco Tomamichel
Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite syste…
Position-Momentum Uncertainty Relations in the Presence of Quantum Memory
Fabian Furrer, Mario Berta, Marco Tomamichel +2
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentu…
Variations on Classical and Quantum Extractors
Mario Berta, Omar Fawzi, Volkher B. Scholz +1
Many constructions of randomness extractors are known to work in the presence of quantum side information, but there also exist extractors which do not [Gavinsky {\it et al.}, STOC…
End-to-end resource analysis for quantum interior point methods and portfolio optimization
Alexander M. Dalzell, B. David Clader, Grant Salton +8
We study quantum interior point methods (QIPMs) for second-order cone programming (SOCP), guided by the example use case of portfolio optimization (PO). We provide a complete quant…
Quantum state preparation without coherent arithmetic
Sam McArdle, András Gilyén, Mario Berta
We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function. Unlike existing approaches, our method does not require handcrafted…
Thermodynamic Capacity of Quantum Processes
Philippe Faist, Mario Berta, Fernando Brandão
Thermodynamics imposes restrictions on what state transformations are possible. In the macroscopic limit of asymptotically many independent copies of a state---as for instance in t…
Optimality of meta-converse for channel simulation
Aadil Oufkir, Omar Fawzi, Mario Berta
We study the effect of shared non-signaling correlations for the problem of simulating a channel using noiseless communication in the one-shot setting. For classical channels, we s…
The Smooth Entropy Formalism for von Neumann Algebras
Mario Berta, Fabian Furrer, Volkher B. Scholz
We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for…
Channel Simulation: Finite Blocklengths and Broadcast Channels
Michael X. Cao, Navneeth Ramakrishnan, Mario Berta +1
We study channel simulation under common randomness assistance in the finite-blocklength regime and identify the smooth channel max-information as a linear program one-shot convers…
Exponents for Shared Randomness-Assisted Channel Simulation
Aadil Oufkir, Michael X. Cao, Hao-Chung Cheng +1
We determine the exact error and strong converse exponents of shared randomness-assisted channel simulation in worst case total-variation distance. Namely, we find that these expon…
Multivariate Trace Inequalities
David Sutter, Mario Berta, Marco Tomamichel
We prove several trace inequalities that extend the Golden-Thompson and the Araki-Lieb-Thirring inequality to arbitrarily many matrices. In particular, we strengthen Lieb's triple…
Rapid Mixing of Quantum Gibbs Samplers for Weakly-Interacting Quantum Systems
Å tÄpán Å mÃd, Richard Meister, Mario Berta +1
Dissipative quantum algorithms for state preparation in many-body systems are increasingly recognised as promising candidates for achieving large quantum advantages in application-…
Entropic Uncertainty Relations and their Applications
Patrick J. Coles, Mario Berta, Marco Tomamichel +1
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual sho…
Umlaut information
Filippo Girardi, Aadil Oufkir, Bartosz Regula +3
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…
A min-entropy uncertainty relation for finite size cryptography
Nelly Huei Ying Ng, Mario Berta, Stephanie Wehner
Apart from their foundational significance, entropic uncertainty relations play a central role in proving the security of quantum cryptographic protocols. Of particular interest ar…
Non-additivity in classical-quantum wiretap channels
Arkin Tikku, Mario Berta, Joseph M. Renes
Due to Csiszar and Koerner, the private capacity of classical wiretap channels has a single-letter characterization in terms of the private information. For quantum wiretap channel…
Resource distillation in convex Gaussian resource theories
Hyejung H. Jee, Carlo Sparaciari, Mario Berta
It is known that distillation in continuous variable resource theories is impossible when restricted to Gaussian states and operations. To overcome this limitation, we enlarge the…
Channel coding against quantum jammers via minimax
Michael X. Cao, Yongsheng Yao, Mario Berta
We introduce a minimax approach for characterizing the capacities of fully quantum arbitrarily varying channels (FQAVCs) under different shared resource models. In contrast to prev…
Sparse random Hamiltonians are quantumly easy
Chi-Fang, Chen, Alexander M. Dalzell +3
A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. For this task, there is a well-studied quantum algorithm that perfor…
Superadditivity for Entanglement-Assisted Communication
Hao-Chung Cheng, Mario Berta
The paper demonstrates that, although the entanglement‑assisted capacity of a quantum channel is additive, the reliability (error exponent) can be strictly superadditive, meaning j…
Distributed Quantum Hypothesis Testing under Zero-rate Communication Constraints
Sreejith Sreekumar, Christoph Hirche, Hao-Chung Cheng +1
The trade-offs between error probabilities in quantum hypothesis testing are by now well-understood in the centralized setting, but much less is known for distributed settings. Her…
Quantum Entropy Prover
Shao-Lun Huang, Tobias Rippchen, Mario Berta
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…
Quantum Brascamp-Lieb Dualities
Mario Berta, David Sutter, Michael Walter
Brascamp-Lieb inequalities are entropy inequalities which have a dual formulation as generalized Young inequalities. In this work, we introduce a fully quantum version of this dual…
Thermal States as Convex Combinations of Matrix Product States
Mario Berta, Fernando G. S. L. Brandao, Jutho Haegeman +2
We study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from rev…
Quantum to Classical Randomness Extractors
Mario Berta, Omar Fawzi, Stephanie Wehner
The goal of randomness extraction is to distill (almost) perfect randomness from a weak source of randomness. When the source yields a classical string X, many extractor constructi…
Convergence monitoring of quantum Gibbs samplers
Nikolaos Louloudis, Ruben Ibarrondo, Mikel Sanz +1
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 rigoro…
Quantum computational complexity of matrix functions
Santiago Cifuentes, Samson Wang, Thais L. Silva +2
We investigate the dividing line between classical and quantum computational power in estimating properties of matrix functions. More precisely, we study the computational complexi…
Chain rules for quantum channels
Mario Berta, Marco Tomamichel
Divergence chain rules for channels relate the divergence of a pair of channel inputs to the divergence of the corresponding channel outputs. An important special case of such a ru…
Moderate deviation expansion for fully quantum tasks
Navneeth Ramakrishnan, Marco Tomamichel, Mario Berta
The moderate deviation regime is concerned with the finite block length trade-off between communication cost and error for information processing tasks in the asymptotic regime, wh…