@article{13266, abstract = {The 3′,5′-cyclic adenosine monophosphate (cAMP) is a versatile second messenger in many mammalian signaling pathways. However, its role in plants remains not well-recognized. Recent discovery of adenylate cyclase (AC) activity for transport inhibitor response 1/auxin-signaling F-box proteins (TIR1/AFB) auxin receptors and the demonstration of its importance for canonical auxin signaling put plant cAMP research back into spotlight. This insight briefly summarizes the well-established cAMP signaling pathways in mammalian cells and describes the turbulent and controversial history of plant cAMP research highlighting the major progress and the unresolved points. We also briefly review the current paradigm of auxin signaling to provide a background for the discussion on the AC activity of TIR1/AFB auxin receptors and its potential role in transcriptional auxin signaling as well as impact of these discoveries on plant cAMP research in general.}, author = {Qi, Linlin and Friml, Jiří}, issn = {1469-8137}, journal = {New Phytologist}, number = {2}, pages = {489--495}, publisher = {Wiley}, title = {{Tale of cAMP as a second messenger in auxin signaling and beyond}}, doi = {10.1111/nph.19123}, volume = {240}, year = {2023}, } @article{13267, abstract = {Three-dimensional (3D) reconstruction of living brain tissue down to an individual synapse level would create opportunities for decoding the dynamics and structure–function relationships of the brain’s complex and dense information processing network; however, this has been hindered by insufficient 3D resolution, inadequate signal-to-noise ratio and prohibitive light burden in optical imaging, whereas electron microscopy is inherently static. Here we solved these challenges by developing an integrated optical/machine-learning technology, LIONESS (live information-optimized nanoscopy enabling saturated segmentation). This leverages optical modifications to stimulated emission depletion microscopy in comprehensively, extracellularly labeled tissue and previous information on sample structure via machine learning to simultaneously achieve isotropic super-resolution, high signal-to-noise ratio and compatibility with living tissue. This allows dense deep-learning-based instance segmentation and 3D reconstruction at a synapse level, incorporating molecular, activity and morphodynamic information. LIONESS opens up avenues for studying the dynamic functional (nano-)architecture of living brain tissue.}, author = {Velicky, Philipp and Miguel Villalba, Eder and Michalska, Julia M and Lyudchik, Julia and Wei, Donglai and Lin, Zudi and Watson, Jake and Troidl, Jakob and Beyer, Johanna and Ben Simon, Yoav and Sommer, Christoph M and Jahr, Wiebke and Cenameri, Alban and Broichhagen, Johannes and Grant, Seth G.N. and Jonas, Peter M and Novarino, Gaia and Pfister, Hanspeter and Bickel, Bernd and Danzl, Johann G}, issn = {1548-7105}, journal = {Nature Methods}, pages = {1256--1265}, publisher = {Springer Nature}, title = {{Dense 4D nanoscale reconstruction of living brain tissue}}, doi = {10.1038/s41592-023-01936-6}, volume = {20}, year = {2023}, } @article{13268, abstract = {We give a simple argument to prove Nagai’s conjecture for type II degenerations of compact hyperkähler manifolds and cohomology classes of middle degree. Under an additional assumption, the techniques yield the conjecture in arbitrary degree. This would complete the proof of Nagai’s conjecture in general, as it was proved already for type I degenerations by Kollár, Laza, Saccà, and Voisin [10] and independently by Soldatenkov [18], while it is immediate for type III degenerations. Our arguments are close in spirit to a recent paper by Harder [8] proving similar results for the restrictive class of good degenerations.}, author = {Huybrechts, D. and Mauri, Mirko}, issn = {1945-001X}, journal = {Mathematical Research Letters}, number = {1}, pages = {125--141}, publisher = {International Press}, title = {{On type II degenerations of hyperkähler manifolds}}, doi = {10.4310/mrl.2023.v30.n1.a6}, volume = {30}, year = {2023}, } @article{13269, abstract = {This paper is a collection of results on combinatorial properties of codes for the Z-channel . A Z-channel with error fraction τ takes as input a length- n binary codeword and injects in an adversarial manner up to n τ asymmetric errors, i.e., errors that only zero out bits but do not flip 0’s to 1’s. It is known that the largest ( L - 1)-list-decodable code for the Z-channel with error fraction τ has exponential size (in n ) if τ is less than a critical value that we call the ( L - 1)- list-decoding Plotkin point and has constant size if τ is larger than the threshold. The ( L -1)-list-decoding Plotkin point is known to be L -1/L-1 – L -L/ L-1 , which equals 1/4 for unique-decoding with L -1 = 1. In this paper, we derive various results for the size of the largest codes above and below the list-decoding Plotkin point. In particular, we show that the largest ( L -1)-list-decodable code ε-above the Plotkin point, for any given sufficiently small positive constant ε > 0, has size Θ L (ε -3/2 ) for any L - 1 ≥ 1. We also devise upper and lower bounds on the exponential size of codes below the list-decoding Plotkin point.}, author = {Polyanskii, Nikita and Zhang, Yihan}, issn = {1557-9654}, journal = {IEEE Transactions on Information Theory}, number = {10}, pages = {6340--6357}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Codes for the Z-channel}}, doi = {10.1109/TIT.2023.3292219}, volume = {69}, year = {2023}, } @article{13270, abstract = {Consider a geodesic triangle on a surface of constant curvature and subdivide it recursively into four triangles by joining the midpoints of its edges. We show the existence of a uniform δ>0 such that, at any step of the subdivision, all the triangle angles lie in the interval (δ,π−δ) . Additionally, we exhibit stabilising behaviours for both angles and lengths as this subdivision progresses.}, author = {Brunck, Florestan R}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, number = {3}, pages = {1059--1089}, publisher = {Springer Nature}, title = {{Iterated medial triangle subdivision in surfaces of constant curvature}}, doi = {10.1007/s00454-023-00500-5}, volume = {70}, year = {2023}, } @article{13271, abstract = {In this paper, we prove the convexity of trace functionals (A,B,C)↦Tr|BpACq|s, for parameters (p, q, s) that are best possible, where B and C are any n-by-n positive-definite matrices, and A is any n-by-n matrix. We also obtain the monotonicity versions of trace functionals of this type. As applications, we extend some results in Carlen et al. (Linear Algebra Appl 490:174–185, 2016), Hiai and Petz (Publ Res Inst Math Sci 48(3):525-542, 2012) and resolve a conjecture in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) in the matrix setting. Other conjectures in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) will also be discussed. We also show that some related trace functionals are not concave in general. Such concavity results were expected to hold in different problems.}, author = {Zhang, Haonan}, issn = {1424-0637}, journal = {Annales Henri Poincare}, publisher = {Springer Nature}, title = {{Some convexity and monotonicity results of trace functionals}}, doi = {10.1007/s00023-023-01345-7}, year = {2023}, } @article{13274, abstract = {Viscous flows through pipes and channels are steady and ordered until, with increasing velocity, the laminar motion catastrophically breaks down and gives way to turbulence. How this apparently discontinuous change from low- to high-dimensional motion can be rationalized within the framework of the Navier-Stokes equations is not well understood. Exploiting geometrical properties of transitional channel flow we trace turbulence to far lower Reynolds numbers (Re) than previously possible and identify the complete path that reversibly links fully turbulent motion to an invariant solution. This precursor of turbulence destabilizes rapidly with Re, and the accompanying explosive increase in attractor dimension effectively marks the transition between deterministic and de facto stochastic dynamics.}, author = {Paranjape, Chaitanya S and Yalniz, Gökhan and Duguet, Yohann and Budanur, Nazmi B and Hof, Björn}, issn = {1079-7114}, journal = {Physical Review Letters}, keywords = {General Physics and Astronomy}, number = {3}, publisher = {American Physical Society}, title = {{Direct path from turbulence to time-periodic solutions}}, doi = {10.1103/physrevlett.131.034002}, volume = {131}, year = {2023}, } @misc{13275, abstract = {We introduce a generic and accessible implementation of an exact diagonalization method for studying few-fermion models. Our aim is to provide a testbed for the newcomers to the field as well as a stepping stone for trying out novel optimizations and approximations. This userguide consists of a description of the algorithm, and several examples in varying orders of sophistication. In particular, we exemplify our routine using an effective-interaction approach that fixes the low-energy physics. We benchmark this approach against the existing data, and show that it is able to deliver state-of-the-art numerical results at a significantly reduced computational cost.}, author = {Rammelmüller, Lukas and Huber, David and Volosniev, Artem}, publisher = {SciPost Foundation}, title = {{Codebase release 1.0 for FermiFCI}}, doi = {10.21468/scipostphyscodeb.12-r1.0}, year = {2023}, } @article{13276, abstract = {We introduce a generic and accessible implementation of an exact diagonalization method for studying few-fermion models. Our aim is to provide a testbed for the newcomers to the field as well as a stepping stone for trying out novel optimizations and approximations. This userguide consists of a description of the algorithm, and several examples in varying orders of sophistication. In particular, we exemplify our routine using an effective-interaction approach that fixes the low-energy physics. We benchmark this approach against the existing data, and show that it is able to deliver state-of-the-art numerical results at a significantly reduced computational cost.}, author = {Rammelmüller, Lukas and Huber, David and Volosniev, Artem}, issn = {2949-804X}, journal = {SciPost Physics Codebases}, publisher = {SciPost Foundation}, title = {{A modular implementation of an effective interaction approach for harmonically trapped fermions in 1D}}, doi = {10.21468/scipostphyscodeb.12}, year = {2023}, } @article{13277, abstract = {Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic processes has been proposed. Here we provide first steps towards the extension of this stochastic approach to bosonic systems by considering the one-dimensional quantum quartic oscillator. We show how to exactly parameterize the time evolution of this prototypical model via the dynamics of a set of classical variables. We interpret these variables as stochastic processes, which allows us to propose a novel way to numerically simulate the time evolution of the system. We benchmark our findings by considering analytically solvable limits and providing alternative derivations of known results.}, author = {Tucci, Gennaro and De Nicola, Stefano and Wald, Sascha and Gambassi, Andrea}, issn = {2666-9366}, journal = {SciPost Physics Core}, keywords = {Statistical and Nonlinear Physics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Condensed Matter Physics}, number = {2}, publisher = {SciPost Foundation}, title = {{Stochastic representation of the quantum quartic oscillator}}, doi = {10.21468/scipostphyscore.6.2.029}, volume = {6}, year = {2023}, } @article{13278, abstract = {We present a numerical analysis of spin-1/2 fermions in a one-dimensional harmonic potential in the presence of a magnetic point-like impurity at the center of the trap. The model represents a few-body analogue of a magnetic impurity in the vicinity of an s-wave superconductor. Already for a few particles we find a ground-state level crossing between sectors with different fermion parities. We interpret this crossing as a few-body precursor of a quantum phase transition, which occurs when the impurity "breaks" a Cooper pair. This picture is further corroborated by analyzing density-density correlations in momentum space. Finally, we discuss how the system may be realized with existing cold-atoms platforms.}, author = {Rammelmüller, Lukas and Huber, David and Čufar, Matija and Brand, Joachim and Hammer, Hans-Werner and Volosniev, Artem}, issn = {2542-4653}, journal = {SciPost Physics}, keywords = {General Physics and Astronomy}, number = {1}, publisher = {SciPost Foundation}, title = {{Magnetic impurity in a one-dimensional few-fermion system}}, doi = {10.21468/scipostphys.14.1.006}, volume = {14}, year = {2023}, } @phdthesis{13286, abstract = {Semiconductor-superconductor hybrid systems are the harbour of many intriguing mesoscopic phenomena. This material combination leads to spatial variations of the superconducting properties, which gives rise to Andreev bound states (ABSs). Some of these states might exhibit remarkable properties that render them highly desirable for topological quantum computing. The most prominent and hunted of such states are Majorana zero modes (MZMs), quasiparticles equals to their own quasiparticles that they follow non-abelian statistics. In this thesis, we first introduce the general framework of such hybrid systems and, then, we unveil a series of mesoscopic phenomena that we discovered. Firstly, we show tunneling spectroscopy experiments on full-shell nanowires (NWs) showing that unwanted quantum-dot states coupled to superconductors (Yu-Shiba-Rusinov states) can mimic MZMs signatures. Then, we introduce a novel protocol which allowed the integration of tunneling spectroscopy with Coulomb spectroscopy within the same device. Employing this approach on both full-shell NWs and partial-shell NWs, we demonstrated that longitudinally confined states reveal charge transport phenomenology similar to the one expected for MZMs. These findings shed light on the intricate interplay between superconductivity and quantum confinement, which brought us to explore another material platform, i.e. a two-dimensional Germanium hole gas. After developing a robust way to induce superconductivity in such system, we showed how to engineer the proximity effect and we revealed a superconducting hard gap. Finally, we created a superconducting radio frequency driven ideal diode and a generator of non-sinusoidal current-phase relations. Our results open the path for the exploration of protected superconducting qubits and more complex hybrid devices in planar Germanium, like Kitaev chains and hybrid qubit devices.}, author = {Valentini, Marco}, issn = {2663 - 337X}, pages = {184}, publisher = {Institute of Science and Technology Austria}, title = {{Mesoscopic phenomena in hybrid semiconductor-superconductor nanodevices : From full-shell nanowires to two-dimensional hole gas in germanium}}, doi = {10.15479/at:ista:13286}, year = {2023}, } @inproceedings{13292, abstract = {The operator precedence languages (OPLs) represent the largest known subclass of the context-free languages which enjoys all desirable closure and decidability properties. This includes the decidability of language inclusion, which is the ultimate verification problem. Operator precedence grammars, automata, and logics have been investigated and used, for example, to verify programs with arithmetic expressions and exceptions (both of which are deterministic pushdown but lie outside the scope of the visibly pushdown languages). In this paper, we complete the picture and give, for the first time, an algebraic characterization of the class of OPLs in the form of a syntactic congruence that has finitely many equivalence classes exactly for the operator precedence languages. This is a generalization of the celebrated Myhill-Nerode theorem for the regular languages to OPLs. As one of the consequences, we show that universality and language inclusion for nondeterministic operator precedence automata can be solved by an antichain algorithm. Antichain algorithms avoid determinization and complementation through an explicit subset construction, by leveraging a quasi-order on words, which allows the pruning of the search space for counterexample words without sacrificing completeness. Antichain algorithms can be implemented symbolically, and these implementations are today the best-performing algorithms in practice for the inclusion of finite automata. We give a generic construction of the quasi-order needed for antichain algorithms from a finite syntactic congruence. This yields the first antichain algorithm for OPLs, an algorithm that solves the ExpTime-hard language inclusion problem for OPLs in exponential time.}, author = {Henzinger, Thomas A and Kebis, Pavol and Mazzocchi, Nicolas Adrien and Sarac, Naci E}, booktitle = {50th International Colloquium on Automata, Languages, and Programming}, isbn = {9783959772785}, issn = {1868-8969}, location = {Paderborn, Germany}, pages = {129:1----129:20}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Regular methods for operator precedence languages}}, doi = {10.4230/LIPIcs.ICALP.2023.129}, volume = {261}, year = {2023}, } @inproceedings{13310, abstract = {Machine-learned systems are in widespread use for making decisions about humans, and it is important that they are fair, i.e., not biased against individuals based on sensitive attributes. We present runtime verification of algorithmic fairness for systems whose models are unknown, but are assumed to have a Markov chain structure. We introduce a specification language that can model many common algorithmic fairness properties, such as demographic parity, equal opportunity, and social burden. We build monitors that observe a long sequence of events as generated by a given system, and output, after each observation, a quantitative estimate of how fair or biased the system was on that run until that point in time. The estimate is proven to be correct modulo a variable error bound and a given confidence level, where the error bound gets tighter as the observed sequence gets longer. Our monitors are of two types, and use, respectively, frequentist and Bayesian statistical inference techniques. While the frequentist monitors compute estimates that are objectively correct with respect to the ground truth, the Bayesian monitors compute estimates that are correct subject to a given prior belief about the system’s model. Using a prototype implementation, we show how we can monitor if a bank is fair in giving loans to applicants from different social backgrounds, and if a college is fair in admitting students while maintaining a reasonable financial burden on the society. Although they exhibit different theoretical complexities in certain cases, in our experiments, both frequentist and Bayesian monitors took less than a millisecond to update their verdicts after each observation.}, author = {Henzinger, Thomas A and Karimi, Mahyar and Kueffner, Konstantin and Mallik, Kaushik}, booktitle = {Computer Aided Verification}, isbn = {9783031377020}, issn = {1611-3349}, location = {Paris, France}, pages = {358–382}, publisher = {Springer Nature}, title = {{Monitoring algorithmic fairness}}, doi = {10.1007/978-3-031-37703-7_17}, volume = {13965}, year = {2023}, } @unpublished{13312, abstract = {Superconductor/semiconductor hybrid devices have attracted increasing interest in the past years. Superconducting electronics aims to complement semiconductor technology, while hybrid architectures are at the forefront of new ideas such as topological superconductivity and protected qubits. In this work, we engineer the induced superconductivity in two-dimensional germanium hole gas by varying the distance between the quantum well and the aluminum. We demonstrate a hard superconducting gap and realize an electrically and flux tunable superconducting diode using a superconducting quantum interference device (SQUID). This allows to tune the current phase relation (CPR), to a regime where single Cooper pair tunneling is suppressed, creating a $ \sin \left( 2 \varphi \right)$ CPR. Shapiro experiments complement this interpretation and the microwave drive allows to create a diode with $ \approx 100 \%$ efficiency. The reported results open up the path towards monolithic integration of spin qubit devices, microwave resonators and (protected) superconducting qubits on a silicon technology compatible platform.}, author = {Valentini, Marco and Sagi, Oliver and Baghumyan, Levon and Gijsel, Thijs de and Jung, Jason and Calcaterra, Stefano and Ballabio, Andrea and Servin, Juan Aguilera and Aggarwal, Kushagra and Janik, Marian and Adletzberger, Thomas and Souto, Rubén Seoane and Leijnse, Martin and Danon, Jeroen and Schrade, Constantin and Bakkers, Erik and Chrastina, Daniel and Isella, Giovanni and Katsaros, Georgios}, booktitle = {arXiv}, keywords = {Mesoscale and Nanoscale Physics}, title = {{Radio frequency driven superconducting diode and parity conserving Cooper pair transport in a two-dimensional germanium hole gas}}, doi = {10.48550/arXiv.2306.07109}, year = {2023}, } @article{13314, abstract = {The emergence of large-scale order in self-organized systems relies on local interactions between individual components. During bacterial cell division, FtsZ—a prokaryotic homologue of the eukaryotic protein tubulin—polymerizes into treadmilling filaments that further organize into a cytoskeletal ring. In vitro, FtsZ filaments can form dynamic chiral assemblies. However, how the active and passive properties of individual filaments relate to these large-scale self-organized structures remains poorly understood. Here we connect single-filament properties with the mesoscopic scale by combining minimal active matter simulations and biochemical reconstitution experiments. We show that the density and flexibility of active chiral filaments define their global order. At intermediate densities, curved, flexible filaments organize into chiral rings and polar bands. An effectively nematic organization dominates for high densities and for straight, mutant filaments with increased rigidity. Our predicted phase diagram quantitatively captures these features, demonstrating how the flexibility, density and chirality of the active filaments affect their collective behaviour. Our findings shed light on the fundamental properties of active chiral matter and explain how treadmilling FtsZ filaments organize during bacterial cell division.}, author = {Dunajova, Zuzana and Prats Mateu, Batirtze and Radler, Philipp and Lim, Keesiang and Brandis, Dörte and Velicky, Philipp and Danzl, Johann G and Wong, Richard W. and Elgeti, Jens and Hannezo, Edouard B and Loose, Martin}, issn = {1745-2481}, journal = {Nature Physics}, pages = {1916--1926}, publisher = {Springer Nature}, title = {{Chiral and nematic phases of flexible active filaments}}, doi = {10.1038/s41567-023-02218-w}, volume = {19}, year = {2023}, } @article{13315, abstract = {How do statistical dependencies in measurement noise influence high-dimensional inference? To answer this, we study the paradigmatic spiked matrix model of principal components analysis (PCA), where a rank-one matrix is corrupted by additive noise. We go beyond the usual independence assumption on the noise entries, by drawing the noise from a low-order polynomial orthogonal matrix ensemble. The resulting noise correlations make the setting relevant for applications but analytically challenging. We provide characterization of the Bayes optimal limits of inference in this model. If the spike is rotation invariant, we show that standard spectral PCA is optimal. However, for more general priors, both PCA and the existing approximate message-passing algorithm (AMP) fall short of achieving the information-theoretic limits, which we compute using the replica method from statistical physics. We thus propose an AMP, inspired by the theory of adaptive Thouless–Anderson–Palmer equations, which is empirically observed to saturate the conjectured theoretical limit. This AMP comes with a rigorous state evolution analysis tracking its performance. Although we focus on specific noise distributions, our methodology can be generalized to a wide class of trace matrix ensembles at the cost of more involved expressions. Finally, despite the seemingly strong assumption of rotation-invariant noise, our theory empirically predicts algorithmic performance on real data, pointing at strong universality properties.}, author = {Barbier, Jean and Camilli, Francesco and Mondelli, Marco and Sáenz, Manuel}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {30}, publisher = {National Academy of Sciences}, title = {{Fundamental limits in structured principal component analysis and how to reach them}}, doi = {10.1073/pnas.2302028120}, volume = {120}, year = {2023}, } @article{13316, abstract = {Although budding yeast has been extensively used as a model organism for studying organelle functions and intracellular vesicle trafficking, whether it possesses an independent endocytic early/sorting compartment that sorts endocytic cargos to the endo-lysosomal pathway or the recycling pathway has long been unclear. The structure and properties of the endocytic early/sorting compartment differ significantly between organisms; in plant cells, the trans-Golgi network (TGN) serves this role, whereas in mammalian cells a separate intracellular structure performs this function. The yeast syntaxin homolog Tlg2p, widely localizing to the TGN and endosomal compartments, is presumed to act as a Q-SNARE for endocytic vesicles, but which compartment is the direct target for endocytic vesicles remained unanswered. Here we demonstrate by high-speed and high-resolution 4D imaging of fluorescently labeled endocytic cargos that the Tlg2p-residing compartment within the TGN functions as the early/sorting compartment. After arriving here, endocytic cargos are recycled to the plasma membrane or transported to the yeast Rab5-residing endosomal compartment through the pathway requiring the clathrin adaptors GGAs. Interestingly, Gga2p predominantly localizes at the Tlg2p-residing compartment, and the deletion of GGAs has little effect on another TGN region where Sec7p is present but suppresses dynamics of the Tlg2-residing early/sorting compartment, indicating that the Tlg2p- and Sec7p-residing regions are discrete entities in the mutant. Thus, the Tlg2p-residing region seems to serve as an early/sorting compartment and function independently of the Sec7p-residing region within the TGN.}, author = {Toshima, Junko Y. and Tsukahara, Ayana and Nagano, Makoto and Tojima, Takuro and Siekhaus, Daria E and Nakano, Akihiko and Toshima, Jiro}, issn = {2050-084X}, journal = {eLife}, publisher = {eLife Sciences Publications}, title = {{The yeast endocytic early/sorting compartment exists as an independent sub-compartment within the trans-Golgi network}}, doi = {10.7554/eLife.84850}, volume = {12}, year = {2023}, } @article{13317, abstract = {We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables in a typical translation invariant system of quantum spins with L-body interactions, where L is the number of spins. This mathematically verifies the observation first made by Santos and Rigol (Phys Rev E 82(3):031130, 2010, https://doi.org/10.1103/PhysRevE.82.031130) that the ETH may hold for systems with additional translational symmetries for a naturally restricted class of observables. We also present numerical support for the same phenomenon for Hamiltonians with local interaction.}, author = {Sugimoto, Shoki and Henheik, Sven Joscha and Riabov, Volodymyr and Erdös, László}, issn = {1572-9613}, journal = {Journal of Statistical Physics}, number = {7}, publisher = {Springer Nature}, title = {{Eigenstate thermalisation hypothesis for translation invariant spin systems}}, doi = {10.1007/s10955-023-03132-4}, volume = {190}, year = {2023}, } @article{13318, abstract = {Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow subexponentially in the degree (Defant et al. in Math Ann 374(1):653–680, 2019). Such inequalities have found great applications in learning low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions, 2022. arXiv preprint arXiv:2209.07279). The conjecture was resolved in Huang et al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894). In this paper, we give a new proof of these Bohnenblust–Hille inequalities for qubit system with constants that are dimension-free and of exponential growth in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials. Using similar ideas, we also study learning problems of low degree quantum observables and Bohr’s radius phenomenon on quantum Boolean cubes.}, author = {Volberg, Alexander and Zhang, Haonan}, issn = {1432-1807}, journal = {Mathematische Annalen}, publisher = {Springer Nature}, title = {{Noncommutative Bohnenblust–Hille inequalities}}, doi = {10.1007/s00208-023-02680-0}, year = {2023}, }