# A. Winter

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NameA. Winter |
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## Pub CategoriesQuantum Physics (40) Computer Science - Information Theory (17) Mathematics - Information Theory (17) Mathematical Physics (9) Mathematics - Mathematical Physics (9) Physics - Statistical Mechanics (6) Mathematics - Probability (4) Mathematics - Combinatorics (3) High Energy Physics - Theory (3) Physics - Mesoscopic Systems and Quantum Hall Effect (2) Mathematics - Operator Algebras (2) Physics - Optics (2) High Energy Physics - Experiment (2) Computer Science - Computational Complexity (2) Physics - Strongly Correlated Electrons (1) Physics - History of Physics (1) Mathematics - Metric Geometry (1) Mathematics - Functional Analysis (1) Physics - Accelerator Physics (1) High Energy Physics - Phenomenology (1) Physics - Soft Condensed Matter (1) Computer Science - Computer Science and Game Theory (1) |

## Publications Authored By A. Winter

Today, the internet makes tremendous amounts of data widely available. Often, the same information is behind multiple different available data sets. This lends growing importance to latent variable models that try to learn the hidden information from the available imperfect versions. Read More

We propose a type-dependent branching model with mutation and competition for modeling phylogenies of a virus population. The competition kernel depends for any two virus particles on the particles' types, the total mass of the population as well as genetic information available through the number of nucleotide substitutions separating the virus particles. We consider the evolving phylogenies of this individual based model in the huge population, short reproduction time and frequent mutation regime, and show tightness in the state space of marked metric measure spaces. Read More

We generalize the recently proposed resource theory of coherence (or superposition) [Baumgratz, Cramer & Plenio, Phys. Rev. Lett. Read More

Many determinantal inequalities for positive definite block matrices are consequences of general entropy inequalities, specialised to Gaussian distributed vectors with prescribed covariances. In particular, strong subadditivity (SSA) yields \begin{equation*} \ln\det V_{AC} + \ln\det V_{BC} - \ln\det V_{ABC} - \ln\det V_C \geq 0 \end{equation*} for all $3\times 3$-block matrices $V_{ABC}$, where subscripts identify principal submatrices. We shall refer to the above inequality as SSA of log-det entropy. Read More

The phenomenon of data hiding, i.e. the existence of pairs of states of a bipartite system that are perfectly distinguishable via general entangled measurements yet almost indistinguishable under LOCC, is a distinctive signature of nonclassicality. Read More

Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. [PRL 113:140401 (2014)], following \AA{}berg [arXiv:quant-ph/0612146], have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Read More

We show that the distillable coherence -- which is equal to the relative entropy of coherence --, is, up to a constant factor, always bounded by the $\ell_1$-norm measure of coherence (defined as the sum of absolute values of off-diagonals). Thus, the latter plays a similar role as logarithmic negativity plays in entanglement theory, and this is the best operational interpretation from a resource-theoretic viewpoint. Consequently the two measures are intimately connected to another operational measure, the robustness of coherence. Read More

Thermodynamics is one of the most successful physical theories ever formulated. Though it was initially developed to deal with steam engines and, in particular, the problem of conversion of heat into mechanical work, it has prevailed even after the scientific revolutions of relativity and quantum mechanics. Despite its wide range of applicability, it is known that the laws of thermodynamics break down when systems are correlated with their environments. Read More

The capability of a given channel to communicate information is, a priori, distinct from its capability to distribute shared randomness. In this article we define randomness distribution capacities of quantum channels assisted by forward, back, or two-way classical communication and compare these to the corresponding communication capacities. With forward assistance or no assistance, we find that they are equal. Read More

We provide new constructions of unitary $t$-designs for general $t$ on one qudit and $N$ qubits, and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time, as a basic framework to investigate randomising time evolution in quantum many-body systems. The new constructions are based on recently proposed schemes of repeating random unitaires diagonal in mutually unbiased bases. We first show that, if a pair of the bases satisfies a certain condition, the process on one qudit approximately forms a unitary $t$-design after $O(t)$ repetitions. Read More

**Authors:**H. Abramowicz, A. Abusleme, K. Afanaciev, N. Alipour Tehrani, C. Balázs, Y. Benhammou, M. Benoit, B. Bilki, J. -J. Blaising, M. J. Boland, M. Boronat, O. Borysov, I. Božović-Jelisavčić, M. Buckland, S. Bugiel, P. N. Burrows, T. K. Charles, W. Daniluk, D. Dannheim, R. Dasgupta, M. Demarteau, M. A. Díaz Gutierrez, G. Eigen, K. Elsener, U. Felzmann, M. Firlej, E. Firu, T. Fiutowski, J. Fuster, M. Gabriel, F. Gaede, I. García, V. Ghenescu, J. Goldstein, S. Green, C. Grefe, M. Hauschild, C. Hawkes, D. Hynds, M. Idzik, G. Kačarević, J. Kalinowski, S. Kananov, W. Klempt, M. Kopec, M. Krawczyk, B. Krupa, M. Kucharczyk, S. Kulis, T. Laštovička, T. Lesiak, A. Levy, I. Levy, L. Linssen, S. Lukić, A. A. Maier, V. Makarenko, J. S. Marshall, K. Mei, G. Milutinović-Dumbelović, J. Moroń, A. Moszczyński, D. Moya, R. M. Münker, A. Münnich, A. T. Neagu, N. Nikiforou, K. Nikolopoulos, A. Nürnberg, M. Pandurović, B. Pawlik, E. Perez Codina, I. Peric, M. Petric, F. Pitters, S. G. Poss, T. Preda, D. Protopopescu, R. Rassool, S. Redford, J. Repond, A. Robson, P. Roloff, E. Ros, O. Rosenblat, A. Ruiz-Jimeno, A. Sailer, D. Schlatter, D. Schulte, N. Shumeiko, E. Sicking, F. Simon, R. Simoniello, P. Sopicki, S. Stapnes, R. Ström, J. Strube, K. P. Świentek, M. Szalay, M. Tesař, M. A. Thomson, J. Trenado, U. I. Uggerhøj, N. van der Kolk, E. van der Kraaij, M. Vicente Barreto Pinto, I. Vila, M. Vogel Gonzalez, M. Vos, J. Vossebeld, M. Watson, N. Watson, M. A. Weber, H. Weerts, J. D. Wells, L. Weuste, A. Winter, T. Wojtoń, L. Xia, B. Xu, A. F. Żarnecki, L. Zawiejski, I. -S. Zgura

The Compact Linear Collider (CLIC) is an option for a future e+e- collider operating at centre-of-mass energies up to 3 TeV, providing sensitivity to a wide range of new physics phenomena and precision physics measurements at the energy frontier. This paper presents the Higgs physics reach of CLIC operating in three energy stages, sqrt(s) = 350 GeV, 1.4 TeV and 3 TeV. Read More

**Authors:**The CLIC, CLICdp collaborations, :, M. J. Boland, U. Felzmann, P. J. Giansiracusa, T. G. Lucas, R. P. Rassool, C. Balazs, T. K. Charles, K. Afanaciev, I. Emeliantchik, A. Ignatenko, V. Makarenko, N. Shumeiko, A. Patapenka, I. Zhuk, A. C. Abusleme Hoffman, M. A. Diaz Gutierrez, M. Vogel Gonzalez, Y. Chi, X. He, G. Pei, S. Pei, G. Shu, X. Wang, J. Zhang, F. Zhao, Z. Zhou, H. Chen, Y. Gao, W. Huang, Y. P. Kuang, B. Li, Y. Li, J. Shao, J. Shi, C. Tang, X. Wu, L. Ma, Y. Han, W. Fang, Q. Gu, D. Huang, X. Huang, J. Tan, Z. Wang, Z. Zhao, T. Laštovička, U. Uggerhoj, T. N. Wistisen, A. Aabloo, K. Eimre, K. Kuppart, S. Vigonski, V. Zadin, M. Aicheler, E. Baibuz, E. Brücken, F. Djurabekova, P. Eerola, F. Garcia, E. Haeggström, K. Huitu, V. Jansson, V. Karimaki, I. Kassamakov, A. Kyritsakis, S. Lehti, A. Meriläinen, R. Montonen, T. Niinikoski, K. Nordlund, K. Österberg, M. Parekh, N. A. Törnqvist, J. Väinölä, M. Veske, W. Farabolini, A. Mollard, O. Napoly, F. Peauger, J. Plouin, P. Bambade, I. Chaikovska, R. Chehab, M. Davier, W. Kaabi, E. Kou, F. LeDiberder, R. Pöschl, D. Zerwas, B. Aimard, G. Balik, J. -P. Baud, J. -J. Blaising, L. Brunetti, M. Chefdeville, C. Drancourt, N. Geoffroy, J. Jacquemier, A. Jeremie, Y. Karyotakis, J. M. Nappa, S. Vilalte, G. Vouters, A. Bernard, I. Peric, M. Gabriel, F. Simon, M. Szalay, N. van der Kolk, T. Alexopoulos, E. N. Gazis, N. Gazis, E. Ikarios, V. Kostopoulos, S. Kourkoulis, P. D. Gupta, P. Shrivastava, H. Arfaei, M. K. Dayyani, H. Ghasem, S. S. Hajari, H. Shaker, Y. Ashkenazy, H. Abramowicz, Y. Benhammou, O. Borysov, S. Kananov, A. Levy, I. Levy, O. Rosenblat, G. D'Auria, S. Di Mitri, T. Abe, A. Aryshev, T. Higo, Y. Makida, S. Matsumoto, T. Shidara, T. Takatomi, Y. Takubo, T. Tauchi, N. Toge, K. Ueno, J. Urakawa, A. Yamamoto, M. Yamanaka, R. Raboanary, R. Hart, H. van der Graaf, G. Eigen, J. Zalieckas, E. Adli, R. Lillestøl, L. Malina, J. Pfingstner, K. N. Sjobak, W. Ahmed, M. I. Asghar, H. Hoorani, S. Bugiel, R. Dasgupta, M. Firlej, T. A. Fiutowski, M. Idzik, M. Kopec, M. Kuczynska, J. Moron, K. P. Swientek, W. Daniluk, B. Krupa, M. Kucharczyk, T. Lesiak, A. Moszczynski, B. Pawlik, P. Sopicki, T. Wojtoń, L. Zawiejski, J. Kalinowski, M. Krawczyk, A. F. Żarnecki, E. Firu, V. Ghenescu, A. T. Neagu, T. Preda, I-S. Zgura, A. Aloev, N. Azaryan, J. Budagov, M. Chizhov, M. Filippova, V. Glagolev, A. Gongadze, S. Grigoryan, D. Gudkov, V. Karjavine, M. Lyablin, A. Olyunin, A. Samochkine, A. Sapronov, G. Shirkov, V. Soldatov, A. Solodko, E. Solodko, G. Trubnikov, I. Tyapkin, V. Uzhinsky, A. Vorozhtov, E. Levichev, N. Mezentsev, P. Piminov, D. Shatilov, P. Vobly, K. Zolotarev, I. Bozovic Jelisavcic, G. Kacarevic, S. Lukic, G. Milutinovic-Dumbelovic, M. Pandurovic, U. Iriso, F. Perez, M. Pont, J. Trenado, M. Aguilar-Benitez, J. Calero, L. Garcia-Tabares, D. Gavela, J. L. Gutierrez, D. Lopez, F. Toral, D. Moya, A. Ruiz Jimeno, I. Vila, T. Argyropoulos, C. Blanch Gutierrez, M. Boronat, D. Esperante, A. Faus-Golfe, J. Fuster, N. Fuster Martinez, N. Galindo Muñoz, I. García, J. Giner Navarro, E. Ros, M. Vos, R. Brenner, T. Ekelöf, M. Jacewicz, J. Ögren, M. Olvegård, R. Ruber, V. Ziemann, D. Aguglia, N. Alipour Tehrani, A. Andersson, F. Andrianala, F. Antoniou, K. Artoos, S. Atieh, R. Ballabriga Sune, M. J. Barnes, J. Barranco Garcia, H. Bartosik, C. Belver-Aguilar, A. Benot Morell, D. R. Bett, S. Bettoni, G. Blanchot, O. Blanco Garcia, X. A. Bonnin, O. Brunner, H. Burkhardt, S. Calatroni, M. Campbell, N. Catalan Lasheras, M. Cerqueira Bastos, A. Cherif, E. Chevallay, B. Constance, R. Corsini, B. Cure, S. Curt, B. Dalena, D. Dannheim, G. De Michele, L. De Oliveira, N. Deelen, J. P. Delahaye, T. Dobers, S. Doebert, M. Draper, F. Duarte Ramos, A. Dubrovskiy, K. Elsener, J. Esberg, M. Esposito, V. Fedosseev, P. Ferracin, A. Fiergolski, K. Foraz, A. Fowler, F. Friebel, J-F. Fuchs, C. A. Fuentes Rojas, A. Gaddi, L. Garcia Fajardo, H. Garcia Morales, C. Garion, L. Gatignon, J-C. Gayde, H. Gerwig, A. N. Goldblatt, C. Grefe, A. Grudiev, F. G. Guillot-Vignot, M. L. Gutt-Mostowy, M. Hauschild, C. Hessler, J. K. Holma, E. Holzer, M. Hourican, D. Hynds, Y. Inntjore Levinsen, B. Jeanneret, E. Jensen, M. Jonker, M. Kastriotou, J. M. K. Kemppinen, R. B. Kieffer, W. Klempt, O. Kononenko, A. Korsback, E. Koukovini Platia, J. W. Kovermann, C-I. Kozsar, I. Kremastiotis, S. Kulis, A. Latina, F. Leaux, P. Lebrun, T. Lefevre, L. Linssen, X. Llopart Cudie, A. A. Maier, H. Mainaud Durand, E. Manosperti, C. Marelli, E. Marin Lacoma, R. Martin, S. Mazzoni, G. Mcmonagle, O. Mete, L. M. Mether, M. Modena, R. M. Münker, T. Muranaka, E. Nebot Del Busto, N. Nikiforou, D. Nisbet, J-M. Nonglaton, F. X. Nuiry, A. Nürnberg, M. Olvegard, J. Osborne, S. Papadopoulou, Y. Papaphilippou, A. Passarelli, M. Patecki, L. Pazdera, D. Pellegrini, K. Pepitone, E. Perez Codina, A. Perez Fontenla, T. H. B. Persson, M. Petrič, F. Pitters, S. Pittet, F. Plassard, R. Rajamak, S. Redford, Y. Renier, S. F. Rey, G. Riddone, L. Rinolfi, E. Rodriguez Castro, P. Roloff, C. Rossi, V. Rude, G. Rumolo, A. Sailer, E. Santin, D. Schlatter, H. Schmickler, D. Schulte, N. Shipman, E. Sicking, R. Simoniello, P. K. Skowronski, P. Sobrino Mompean, L. Soby, M. P. Sosin, S. Sroka, S. Stapnes, G. Sterbini, R. Ström, I. Syratchev, F. Tecker, P. A. Thonet, L. Timeo, H. Timko, R. Tomas Garcia, P. Valerio, A. L. Vamvakas, A. Vivoli, M. A. Weber, R. Wegner, M. Wendt, B. Woolley, W. Wuensch, J. Uythoven, H. Zha, P. Zisopoulos, M. Benoit, M. Vicente Barreto Pinto, M. Bopp, H. H. Braun, M. Csatari Divall, M. Dehler, T. Garvey, J. Y. Raguin, L. Rivkin, R. Zennaro, A. Aksoy, Z. Nergiz, E. Pilicer, I. Tapan, O. Yavas, V. Baturin, R. Kholodov, S. Lebedynskyi, V. Miroshnichenko, S. Mordyk, I. Profatilova, V. Storizhko, N. Watson, A. Winter, J. Goldstein, S. Green, J. S. Marshall, M. A. Thomson, B. Xu, W. A. Gillespie, R. Pan, M. A Tyrk, D. Protopopescu, A. Robson, R. Apsimon, I. Bailey, G. Burt, D. Constable, A. Dexter, S. Karimian, C. Lingwood, M. D. Buckland, G. Casse, J. Vossebeld, A. Bosco, P. Karataev, K. Kruchinin, K. Lekomtsev, L. Nevay, J. Snuverink, E. Yamakawa, V. Boisvert, S. Boogert, G. Boorman, S. Gibson, A. Lyapin, W. Shields, P. Teixeira-Dias, S. West, R. Jones, N. Joshi, R. Bodenstein, P. N. Burrows, G. B. Christian, D. Gamba, C. Perry, J. Roberts, J. A. Clarke, N. A. Collomb, S. P. Jamison, B. J. A. Shepherd, D. Walsh, M. Demarteau, J. Repond, H. Weerts, L. Xia, J. D. Wells, C. Adolphsen, T. Barklow, M. Breidenbach, N. Graf, J. Hewett, T. Markiewicz, D. McCormick, K. Moffeit, Y. Nosochkov, M. Oriunno, N. Phinney, T. Rizzo, S. Tantawi, F. Wang, J. Wang, G. White, M. Woodley

The Compact Linear Collider (CLIC) is a multi-TeV high-luminosity linear e+e- collider under development. For an optimal exploitation of its physics potential, CLIC is foreseen to be built and operated in a staged approach with three centre-of-mass energy stages ranging from a few hundred GeV up to 3 TeV. The first stage will focus on precision Standard Model physics, in particular Higgs and top-quark measurements. Read More

We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This allows us to prove general results on the monogamy of entanglement and steering quantifiers in continuous variable systems with an arbitrary number of modes per party. A powerful hierarchical relation for correlation measures based on the log-determinant of covariance matrices is further established for all Gaussian states, which has no counterpart among quantities based on the conventional von Neumann entropy. Read More

De Finetti theorems show how sufficiently exchangeable states are well-approximated by convex combinations of i.i.d. Read More

Drawing on ideas from game theory and quantum physics, we investigate nonlocal correlations from the point of view of equilibria in games of incomplete information. These equilibria can be classified in decreasing power as general communication equilibria, belief-invariant equilibria and correlated equilibria, all of which contain the familiar Nash equilibria. The notion of belief-invariant equilibrium has appeared in game theory before, in the 1990s. Read More

We present a framework for studying bosonic non-Gaussian channels of continuous-variable systems. Our emphasis is on a class of channels that we call photon-added Gaussian channels which are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian domain for numerous tasks in continuous-variable quantum information processing like entanglement distillation from Gaussian states and universal quantum computation. Read More

"Is entanglement monogamous?" asks the title of a popular article [B. Terhal, IBM J. Res. Read More

Understanding the resource consumption in distributed scenarios is one of the main goals of quantum information theory. A prominent example for such a scenario is the task of quantum state merging where two parties aim to merge their parts of a tripartite quantum state. In standard quantum state merging, entanglement is considered as an expensive resource, while local quantum operations can be performed at no additional cost. Read More

Matter-wave interferometry has become an essential tool in studies on the foundations of quantum physics and for precision measurements. Mechanical gratings have played an important role as coherent beamsplitters for atoms, molecules and clusters since the basic diffraction mechanism is the same for all particles. However, polarizable objects may experience van der Waals shifts when they pass the grating walls and the undesired dephasing may prevent interferometry with massive objects. Read More

A quantum channel physically is a unitary interaction between the information carrying system and an environment, which is initialized in a pure state before the interaction. Conventionally, this state, as also the parameters of the interaction, is assumed to be fixed and known to the sender and receiver. Here, following the model introduced by us earlier [Karumanchi et al. Read More

In the vein of the recent "pretty strong" converse for the quantum and private capacity of degradable quantum channels [Morgan/Winter, IEEE Trans. Inf. Theory 60(1):317-333, 2014], we use the same techniques, in particular the calculus of min-entropies, to show a pretty strong converse for the private capacity of degraded classical-quantum-quantum (cqq-)wiretap channels, which generalize Wyner's model of the degraded classical wiretap channel. Read More

The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented by operators that fail to commute. Read More

The data processing inequality states that the quantum relative entropy between two states $\rho$ and $\sigma$ can never increase by applying the same quantum channel $\mathcal{N}$ to both states. This inequality can be strengthened with a remainder term in the form of a distance between $\rho$ and the closest recovered state $(\mathcal{R} \circ \mathcal{N})(\rho)$, where $\mathcal{R}$ is a recovery map with the property that $\sigma = (\mathcal{R} \circ \mathcal{N})(\sigma)$. We show the existence of an explicit recovery map that is universal in the sense that it depends only on $\sigma$ and the quantum channel $\mathcal{N}$ to be reversed. Read More

We address the problem of understanding from first principles the conditions under which a closed quantum system equilibrates rapidly with respect to a concrete observable. Previously known general upper bounds on the time scales of equilibration were extremely long, with times scaling linearly with the dimension of the Hilbert space. Moreover, these bounds proved to be tight, since particular constructions of observables scaling in this way were found. Read More

We investigate decoupling, one of the most important primitives in quantum Shannon theory, by replacing the uniformly distributed random unitaries commonly used to achieve the protocol, with alternate applications of random unitaries diagonal in the Pauli-$Z$ and -$X$ bases. This strategy was recently shown to achieve an approximate unitary $2$-design after a number of repetitions of the process, which implies that the strategy gradually achieves decoupling. Here, we prove that even fewer repetitions of the process suffice to achieve decoupling, showing that unitary $2$-designs with rather imprecise approximations can achieve decoupling at the same rate as that with the uniform ones. Read More

We consider a spatial multi-type branching model in which individuals migrate in geographic space according to random walks and reproduce according to a state-dependent branching mechanism which can be sub-, super- or critical depending on the local intensity of individuals of the different types. The model is a Lotka-Volterra type model with a spatial component and is related to two models studied in \cite{BlathEtheridgeMeredith2007} as well as to earlier work in \cite{Etheridge2004} and in \cite{NeuhauserPacala1999}. Our main focus is on the diffusion limit of small mass, locally many individuals and rapid reproduction. Read More

The sphere packing bound, in the form given by Shannon, Gallager and Berlekamp, was recently extended to classical-quantum channels, and it was shown that this creates a natural setting for combining probabilistic approaches with some combinatorial ones such as the Lov\'asz theta function. In this paper, we extend the study to the case of constant composition codes. We first extend the sphere packing bound for classical-quantum channels to this case, and we then show that the obtained result is related to a variation of the Lov\'asz theta function studied by Marton. Read More

We study the evolution of genealogies of a population of individuals, whose type frequencies result in an interacting Fleming-Viot process on $\Z$. We construct and analyze the genealogical structure of the population in this genealogy-valued Fleming-Viot process as a marked metric measure space, with each individual carrying its spatial location as a mark. We then show that its time evolution converges to that of the genealogy of a continuum-sites stepping stone model on $\R$, if space and time are scaled diffusively. Read More

**Authors:**Andreas Winter

We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: First, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible form that depends only on the system dimension and the trace distance of the states. Almost the same proof can be used to derive similar continuity bounds for the relative entropy distance from a convex set of states or positive operators. As applications we give new proofs, with tighter bounds, of the asymptotic continuity of the relative entropy of entanglement, $E_R$, and its regularization $E_R^\infty$, as well as of the entanglement of formation, $E_F$. Read More

We establish an operational theory of coherence (or of superposition) in quantum systems, by focusing on the optimal rate of performance of certain tasks. Namely, we introduce the two basic concepts - "coherence distillation" and "coherence cost" in the processing quantum states under so-called incoherent operations [Baumgratz/Cramer/Plenio, Phys. Rev. Read More

We use a recently discovered constrained de Finetti reduction (aka "Post-Selection Lemma") to study the parallel repetition of multi-player non-local games under no-signalling strategies. Since the technique allows us to reduce general strategies to independent plays, we obtain parallel repetition (corresponding to winning all rounds) in the same way as exponential concentration of the probability to win a fraction larger than the value of the game. Our proof technique leads us naturally to a relaxation of no-signalling (NS) strategies, which we dub sub-no-signalling (SNOS). Read More

RoboClam is a burrowing technology inspired by Ensis directus, the Atlantic razor clam. Atlantic razor clams should only be strong enough to dig a few centimeters into the soil, yet they burrow to over 70 cm. The animal uses a clever trick to achieve this: by contracting its body, it agitates and locally fluidizes the soil, reducing the drag and energetic cost of burrowing. Read More

We show that for any graph $G$, by considering "activation" through the strong product with another graph $H$, the relation $\alpha(G) \leq \vartheta(G)$ between the independence number and the Lov\'{a}sz number of $G$ can be made arbitrarily tight: Precisely, the inequality \[ \alpha(G \times H) \leq \vartheta(G \times H) = \vartheta(G)\,\vartheta(H) \] becomes asymptotically an equality for a suitable sequence of ancillary graphs $H$. This motivates us to look for other products of graph parameters of $G$ and $H$ on the right hand side of the above relation. For instance, a result of Rosenfeld and Hales states that \[ \alpha(G \times H) \leq \alpha^*(G)\,\alpha(H), \] with the fractional packing number $\alpha^*(G)$, and for every $G$ there exists $H$ that makes the above an equality; conversely, for every graph $H$ there is a $G$ that attains equality. Read More

We introduce potential capacities of quantum channels in an operational way and provide upper bounds for these quantities, which quantify the ultimate limit of usefulness of a channel for a given task in the best possible context. Unfortunately, except for a few isolated cases, potential capacities seem to be as hard to compute as their "plain" analogues. We thus study upper bounds on some potential capacities: For the classical capacity, we give an upper bound in terms of the entanglement of formation. Read More

Entanglement is a ubiquitous feature of low temperature systems and believed to be highly relevant for the dynamics of condensed matter properties and quantum computation even at higher temperatures. The experimental certification of this paradigmatic quantum effect in macroscopic high temperature systems is constrained by the limited access to the quantum state of the system. In this paper we show how macroscopic observables beyond the energy of the system can be exploited as proxy witnesses for entanglement detection. Read More

Unitary 2-designs are random unitaries simulating up to the second order statistical moments of the uniformly distributed random unitaries, often referred to as Haar random unitaries. They are used in a wide variety of theoretical and practical quantum information protocols, and also have been used to model the dynamics in complex quantum many-body systems. Here, we show that unitary 2-designs can be approximately implemented by alternately repeating random unitaries diagonal in the Pauli-$Z$ basis and that in the Pauli-$X$ basis. Read More

We initiate the study of zero-error communication via quantum channels when the receiver and sender have at their disposal a noiseless feedback channel of unlimited quantum capacity, generalizing Shannon's zero-error communication theory with instantaneous feedback. We first show that this capacity is a function only of the linear span of Choi-Kraus operators of the channel, which generalizes the bipartite equivocation graph of a classical channel, and which we dub "non-commutative bipartite graph". Then we go on to show that the feedback-assisted capacity is non-zero (with constant activating noiseless communication) if and only if the non-commutative bipartite graph is non-trivial, and give a number of equivalent characterizations. Read More

Among several tasks in Machine Learning, a specially important one is that of inferring the latent variables of a system and their causal relations with the observed behavior. Learning a Hidden Markov Model of given stochastic process is a textbook example, known as the positive realization problem (PRP). The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and positive systems theory. Read More

Degradable quantum channels are an important class of completely positive trace-preserving maps. Among other properties, they offer a single-letter formula for the quantum and the private classical capacity and are characterized by the fact that the complementary channel can be obtained from the channel by applying a degrading map. In this work we introduce the concept of approximate degradable channels, which satisfy this condition up to some finite $\varepsilon\geq 0$. Read More

In this paper we consider the problem of generating arbitrary three-party correlations from a combination of public and secret correlations. Two parties -- called Alice and Bob -- share perfectly correlated bits that are secret from a collaborating third party, Charlie. At the same time, all three parties have access to a separate source of correlated bits, and their goal is to convert these two resources into multiple copies of some given tripartite distribution $P_{XYZ}$. Read More

Squashed entanglement [Christandl/Winter, JMP 45(3):829-840 (2004)] is a monogamous entanglement measure, which implies that highly extendible states have small value of the squashed entanglement. Here, invoking a recent inequality for the quantum conditional mutual information [Fawzi/Renner, arXiv:1410.0664, greatly extended and simplified in various work since, up to the most recent contributions of Wilde, arXiv:1505. Read More

We study the one-shot zero-error classical capacity of a quantum channel assisted by quantum no-signalling correlations, and the reverse problem of exact simulation of a prescribed channel by a noiseless classical one. Quantum no-signalling correlations are viewed as two-input and two-output completely positive and trace preserving maps with linear constraints enforcing that the device cannot signal. Both problems lead to simple semidefinite programmes (SDPs) that depend only on the Kraus operator space of the channel. Read More

In this correspondence we present a new proof of Holevo's coding theorem for transmitting classical information through quantum channels, and its strong converse. The technique is largely inspired by Wolfowitz's combinatorial approach using types of sequences. As a by-product of our approach which is independent of previous ones, both in the coding theorem and the converse, we can give a new proof of Holevo's information bound. Read More

We consider multiple non-interacting quantum mechanical two-level systems coupled to a common bosonic bath and study its quantum phase transition with Monte Carlo simulations using a continuous imaginary time cluster algorithm. The common bath induces an effective ferromagnetic interaction between the otherwise independent two-level systems, which can be quantified by an effective interaction strength. For degenerate energy levels above a critical value of the bath coupling strength $\alpha$ all two-level systems freeze into the same state and the critical value $\alpha_c$ decreases asymptotically as $1/N$ with increasing $N$. Read More

The possibility to test experimentally the Bell-Kochen-Specker theorem is
investigated critically, following the demonstrations by Meyer, Kent and
Clifton-Kent that the predictions of quantum mechanics are indistinguishable
(up to arbitrary precision) from those of a non-contextual model, and the
subsequent debate to which extent these models are actually classical or
non-contextual.
The present analysis starts from a careful consideration these
"finite-precision" approximations. A stronger condition for non-contextual
models, dubbed

We initiate the study of passive environment-assisted communication via a quantum channel, modeled as a unitary interaction between the information carrying system and an environment. In this model, the environment is controlled by a benevolent helper who can set its initial state such as to assist sender and receiver of the communication link. (The case of a malicious environment, also known as jammer, or arbitrarily varying channel, is essentially well-understood and comprehensively reviewed. Read More

We develop further the new versions of quantum chromatic numbers of graphs introduced by the first and fourth authors. We prove that the problem of computation of the commuting quantum chromatic number of a graph is solvable by an SDP algorithm and describe an hierarchy of variants of the commuting quantum chromatic number which converge to it. We introduce the tracial rank of a graph, a parameter that gives a lower bound for the commuting quantum chromatic number and parallels the projective rank, and prove that it is multiplicative. Read More

In Athreya, L\"ohr, Winter (2016), an invariance principle is stated for a class of strong Markov processes on tree-like metric measure spaces. It is shown that if the underlying spaces converge Gromov vaguely, then the processes converge in the sense of finite dimensional distributions. Further, if the underlying spaces converge Gromov-Hausdorff vaguely, then the processes converge weakly in path space. Read More

We revisit a fundamental open problem in quantum information theory, namely whether it is possible to transmit quantum information at a rate exceeding the channel capacity if we allow for a non-vanishing probability of decoding error. Here we establish that the Rains information of any quantum channel is a strong converse rate for quantum communication: For any sequence of codes with rate exceeding the Rains information of the channel, we show that the fidelity vanishes exponentially fast as the number of channel uses increases. This remains true even if we consider codes that perform classical post-processing on the transmitted quantum data. Read More

We present a route to non-destructive functionalization of graphene via assembly of vertical all-carbon van der Waals heterostructures. To this end, we employ singlelayer graphene (SLG) sheets grown by low-pressure methane CVD on Cu foils and large-area dielectric ~1 nm thick amino-terminated carbon nanomembranes (NH2-CNMs) generated by electron-beam-induced crosslinking of aromatic self-assembled monolayers. We encapsulate SLG sheets on oxidized silicon wafers with NH2-CNMs via mechanical stacking and characterize structural, chemical and electronic properties of the formed heterostructures by Raman spectroscopy and X-ray photoelectron spectroscopy as well as by electric and electromagnetic transport measurements. Read More