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**Published in:** LIPIcs, Volume 44, 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)

The capability of a given channel to transmit information is, a priori, distinct from its capability to distribute random correlations. Despite that, for classical channels, the capacity to distribute information and randomness turns out to be the same, even with the assistance of auxiliary communication. In this work we show that this is no longer true for quantum channels when feedback is allowed. We prove this by constructing a channel that is noisy for the transmission of information but behaves as a virtual noiseless channel for randomness distribution when assisted by feedback communication. Our result can be seen as a way of unlocking quantum randomness internal to the channel.

Raul Garcia-Patron, William Matthews, and Andreas Winter. Quantum Enhancement of Randomness Distribution. In 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 44, pp. 180-190, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{garciapatron_et_al:LIPIcs.TQC.2015.180, author = {Garcia-Patron, Raul and Matthews, William and Winter, Andreas}, title = {{Quantum Enhancement of Randomness Distribution}}, booktitle = {10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)}, pages = {180--190}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-96-5}, ISSN = {1868-8969}, year = {2015}, volume = {44}, editor = {Beigi, Salman and K\"{o}nig, Robert}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2015.180}, URN = {urn:nbn:de:0030-drops-55567}, doi = {10.4230/LIPIcs.TQC.2015.180}, annote = {Keywords: Quantum Shannon theory, noisy channels, capacity, randomness} }

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**Published in:** LIPIcs, Volume 44, 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)

Unitary 2-designs are random unitary matrices which, in contrast to their Haar-distributed counterparts, have been shown to be efficiently realized by quantum circuits. Most notably, unitary 2-designs are known to achieve decoupling, a fundamental primitive of paramount importance in quantum Shannon theory. Here we prove that unitary 2-designs can be implemented approximately using random diagonal-unitaries.

Yoshifumi Nakata, Christoph Hirche, Ciara Morgan, and Andreas Winter. Implementing Unitary 2-Designs Using Random Diagonal-unitary Matrices. In 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 44, pp. 191-205, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{nakata_et_al:LIPIcs.TQC.2015.191, author = {Nakata, Yoshifumi and Hirche, Christoph and Morgan, Ciara and Winter, Andreas}, title = {{Implementing Unitary 2-Designs Using Random Diagonal-unitary Matrices}}, booktitle = {10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)}, pages = {191--205}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-96-5}, ISSN = {1868-8969}, year = {2015}, volume = {44}, editor = {Beigi, Salman and K\"{o}nig, Robert}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2015.191}, URN = {urn:nbn:de:0030-drops-55570}, doi = {10.4230/LIPIcs.TQC.2015.191}, annote = {Keywords: unitary 2-designs, commuting quantum circuits} }

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**Published in:** LIPIcs, Volume 27, 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)

We study zero-error entanglement assisted source-channel coding (communication in the presence of side information). Adapting a technique of Beigi, we show that such coding requires existence of a set of vectors satisfying orthogonality conditions related to suitably defined graphs G and H. Such vectors exist if and only if theta(G) <= theta(H) where theta represents the Lovász number. We also obtain similar inequalities for the related Schrijver theta^- and Szegedy theta^+ numbers.
These inequalities reproduce several known bounds and also lead to new results. We provide a lower bound on the entanglement assisted cost rate. We show that the entanglement assisted independence number is bounded by the Schrijver number: alpha^*(G) <= theta^-(G). Therefore, we are able to disprove the conjecture that the one-shot entanglement-assisted zero-error capacity is equal to the integer part of the Lovász number. Beigi introduced a quantity beta as an upper bound on alpha^* and posed the question of whether beta(G) = \lfloor theta(G) \rfloor. We answer this in the affirmative and show that a related quantity is equal to \lceil theta(G) \rceil. We show that a quantity chi_{vect}(G) recently introduced in the context of Tsirelson's conjecture is equal to \lceil theta^+(G) \rceil.

Toby Cubitt, Laura Mancinska, David Roberson, Simone Severini, Dan Stahlke, and Andreas Winter. Bounds on Entanglement Assisted Source-channel Coding Via the Lovász Theta Number and Its Variants. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 48-51, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{cubitt_et_al:LIPIcs.TQC.2014.48, author = {Cubitt, Toby and Mancinska, Laura and Roberson, David and Severini, Simone and Stahlke, Dan and Winter, Andreas}, title = {{Bounds on Entanglement Assisted Source-channel Coding Via the Lov\'{a}sz Theta Number and Its Variants}}, booktitle = {9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)}, pages = {48--51}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-73-6}, ISSN = {1868-8969}, year = {2014}, volume = {27}, editor = {Flammia, Steven T. and Harrow, Aram W.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.48}, URN = {urn:nbn:de:0030-drops-48054}, doi = {10.4230/LIPIcs.TQC.2014.48}, annote = {Keywords: source-channel coding, zero-error capacity, Lov\'{a}sz theta} }

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**Published in:** LIPIcs, Volume 27, 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)

A strong converse theorem for channel capacity establishes that the error probability in any communication scheme for a given channel necessarily tends to one if the rate of communication exceeds the channel's capacity. Establishing such a theorem for the quantum capacity of degradable channels has been an elusive task, with the strongest progress so far being a so-called "pretty strong converse." In this work, Morgan and Winter proved that the quantum error of any quantum communication scheme for a given degradable channel converges to a value larger than 1/sqrt(2) in the limit of many channel uses if the quantum rate of communication exceeds the channel's quantum capacity. The present paper establishes a theorem that is a counterpart to this "pretty strong converse." We prove that the large fraction of codes having a rate exceeding the erasure channel's quantum capacity have a quantum error tending to one in the limit of many channel uses. Thus, our work adds to the body of evidence that a fully strong converse theorem should hold for the quantum capacity of the erasure channel. As a side result, we prove that the classical capacity of the quantum erasure channel obeys the strong converse property.

Mark M. Wilde and Andreas Winter. Strong Converse for the Quantum Capacity of the Erasure Channel for Almost All Codes. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 52-66, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{wilde_et_al:LIPIcs.TQC.2014.52, author = {Wilde, Mark M. and Winter, Andreas}, title = {{Strong Converse for the Quantum Capacity of the Erasure Channel for Almost All Codes}}, booktitle = {9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)}, pages = {52--66}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-73-6}, ISSN = {1868-8969}, year = {2014}, volume = {27}, editor = {Flammia, Steven T. and Harrow, Aram W.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.52}, URN = {urn:nbn:de:0030-drops-48068}, doi = {10.4230/LIPIcs.TQC.2014.52}, annote = {Keywords: strong converse, quantum erasure channel, quantum capacity} }

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**Published in:** LIPIcs, Volume 27, 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)

Among several tasks in Machine Learning, is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of such problem is the task of inferring the Hidden Markov Model underlying a given stochastic process. This is known as the positive realization problem (PRP) [Benvenuti,Farina(2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory [Luenberger(1979)].
We consider the scenario where the latent variables are quantum (e.g., quantum states of a finite-dimensional system), and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument-if any-yields the process at hand by iterative application.
We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the Hidden Markov Model, or the iterated quantum instrument, is however devoid from any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The Completely-Positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists.
We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [Guta(2011), Guta&Yamamoto(2013)].

Alex Monras and Andreas Winter. Quantum Learning of Classical Stochastic Processes: The Completely-Positive Realization Problem. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 99-109, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{monras_et_al:LIPIcs.TQC.2014.99, author = {Monras, Alex and Winter, Andreas}, title = {{Quantum Learning of Classical Stochastic Processes: The Completely-Positive Realization Problem}}, booktitle = {9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)}, pages = {99--109}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-73-6}, ISSN = {1868-8969}, year = {2014}, volume = {27}, editor = {Flammia, Steven T. and Harrow, Aram W.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.99}, URN = {urn:nbn:de:0030-drops-48100}, doi = {10.4230/LIPIcs.TQC.2014.99}, annote = {Keywords: quantum instrument, hidden Markov model, machine learning, quantum measurement} }

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**Published in:** LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)

We investigate the universal linear inequalities that hold for the von Neumann entropies in a multi-party system, prepared in a stabiliser state. We demonstrate here that entropy vectors for stabiliser states satisfy, in addition to the classic inequalities, a type of linear rank inequalities associated with the combinatorial structure of normal subgroups of certain matrix groups. In the 4-party case, there is only one such inequality, the so-called Ingleton inequality. For these systems we show that strong subadditivity, weak monotonicity and Ingleton inequality exactly characterize the entropy cone for stabiliser states.

Noah Linden, Frantisek Matus, Mary Beth Ruskai, and Andreas Winter. The Quantum Entropy Cone of Stabiliser States. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 270-284, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{linden_et_al:LIPIcs.TQC.2013.270, author = {Linden, Noah and Matus, Frantisek and Ruskai, Mary Beth and Winter, Andreas}, title = {{The Quantum Entropy Cone of Stabiliser States}}, booktitle = {8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)}, pages = {270--284}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-55-2}, ISSN = {1868-8969}, year = {2013}, volume = {22}, editor = {Severini, Simone and Brandao, Fernando}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.270}, URN = {urn:nbn:de:0030-drops-43278}, doi = {10.4230/LIPIcs.TQC.2013.270}, annote = {Keywords: Entropy inequalities, Stabiliser states, Ingleton inequality} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 5161, Transformation Techniques in Software Engineering (2006)

TrafoDagstuhl brought together representatives of the research
communities in re-engineering, XML processing, model-driven
architecture and other areas of software engineering that involve
grammar- or schema-driven transformations. These various existing
fields and application contexts involve widely varying transformation
techniques – the tradeoffs of which are worth analysing. This
seminar initiated a process of understanding each other's
transformation techniques – their use cases, corresponding methods,
tool support, best practises, and open problems. This process makes it
possible to exchange knowledge and experience between these various
communities. This effort should also help in transposing
transformation concepts from established application fields to new
fields.
This executive summary reports on the conception of the seminar, the
program, outcomes and future work. Most of the material from the
seminar (including abstracts of all talks) as well as additional
papers can be found on the dedicated web site:
http://www.dagstuhl.de/05161/

James R. Cordy, Ralf Lämmel, and Andreas Winter. 05161 Executive Summary – Transformation Techniques in Software Engineering. In Transformation Techniques in Software Engineering. Dagstuhl Seminar Proceedings, Volume 5161, pp. 1-24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{cordy_et_al:DagSemProc.05161.1, author = {Cordy, James R. and L\"{a}mmel, Ralf and Winter, Andreas}, title = {{05161 Executive Summary – Transformation Techniques in Software Engineering}}, booktitle = {Transformation Techniques in Software Engineering}, pages = {1--24}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2006}, volume = {5161}, editor = {James R. Cordy and Ralf L\"{a}mmel and Andreas Winter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05161.1}, URN = {urn:nbn:de:0030-drops-4978}, doi = {10.4230/DagSemProc.05161.1}, annote = {Keywords: Program transformation, transformational programming, generative programming, generative language technology, automated software testing, engineering of metamodels, engineering for XML schemas, engineering of data models} }

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