(Composing Quantum Channels) is an ERA-Net CHIST-ERA
project granted in 2011 and funded by the German Bundesministerium für Bildung und Forschung
, the Swiss National Science Foundation
and the Spanish Ministerio de Ciencia e Innovacion
The power of information theory – classical as well as quantum – originates in the abstraction of information from its physical carrier. On this level of discussion, every process, every time evolution and every operation is described by a quantum channel – an input-output relation abstracting from the microscopic origin of the physical dynamics. Quantum channels are therefore central objects and basic building blocks in quantum information theory. The composition of quantum channels is a very natural operation arising in most physical situations. Sequential composition arises, for instance, when two quantum processes are carried out one after the other. It is therefore surprising that a systematic study is still missing that analyses the effect of composition on basic properties of quantum channels, such as the ability to reliably transmit quantum information.
With this project we propose to fill this gap and provide a first in-depth analysis of fundamental properties of quantum channels, with a particular emphasis on the behaviour under sequential and parallel composition. We will, furthermore, initiate the study of complexity-theoretic properties of quantum channels, thereby providing a novel computer science perspective on quantum channels.
We expect the results from this project to have a profound impact to the study of quantum spin chains, quantum complexity theory and quantum cryptography. The project as well as the consortium is of interdisciplinary nature and will use modern tools from operator space theory, signal processing, convex geometry and complexity theory.
- For an introduction to quantum channels see here.
-  Michael M. Wolf, Toby S. Cubitt, David Perez-Garcia, Are problems in Quantum Information Theory (un)decidable?, preprint arXiv:1111.5425 [quant-ph]
-  Daniel Lercher, Géza Giedke, Michael M. Wolf, Super-activation for Gaussian channels requires squeezing, preprint arXiv:1209.5574 [quant-ph]
-  Andrea Cadarso, Mikel Sanz, Michael M. Wolf, J. Ignacio Cirac, David Perez-Garcia, Entanglement, fractional magnetization and long-range interactions, Phys. Rev. B 87, 035114 (2013)
-  Oleg Szehr, Michael M. Wolf, Perturbation Bounds for Quantum Markov Processes and their Fixed Points, preprint arXiv:1210.1171 [math-ph]
-  Carlos Fernández-González, Norbert Schuch, Michael M. Wolf, J. Ignacio Cirac, David Pérez-García, Frustration free gapless Hamiltonians for Matrix Product States, preprint arXiv:1210.6613 [quant-ph]
-  Teiko Heinosaari, Maria A. Jivulescu, David Reeb, Michael M. Wolf, Extending quantum operations, J. Math. Phys. 53, 102208 (2012)
-  M. J. Kastoryano, M. M. Wolf, J. Eisert, Precisely timing dissipative quantum information processing, preprint arXiv:1205.0985 [quant-ph]
-  Motohisa Fukuda, Piotr Śniady, Partial transpose of random quantum states, Weingarten calculus and meanders, preprint arXiv:1211.1525 [math-ph]
-  Motohisa Fukuda, Ion Nechita, Asymptotically well-behaved input states do not violate additivity for conjugate pairs of random quantum channels, preprint arXiv:1212.1630 [math-ph]
-  Michael J. Kastoryano, David Reeb, Michael M. Wolf, A Cutoff Phenomenon for Quantum Markov Chains, J. Phys. A: Math. Theor. 45, 075307 (2012)
-  Oleg Szehr, David Reeb, Michael M. Wolf, Spectral convergence bounds for classical and quantum Markov processes, preprint arXiv:1301.4827 [math-ph]
-  Matthias Buchinger, Decision problems for non-commutatove stochastic processes, Master-Arbeit TUM 2013
-  Alexander Müller-Hermes, Transposition in Quantum Information Theory, Master-Arbeit, TUM 2012
-  Thorsten B. Wahl, David Perez-Garcia, J. Ignacio Cirac, Matrix Product States with long-range Localizable Entanglement (2012)
-  B. Collins, C. E. Gonzalez-Guillen, D. Perez-Garcia, Matrix Product States, Random Matrix Theory and the Principle of Maximum Entropy, arxiv:1201.6324 (t.b.p. in Commun. Math. Phys.)
-  T. Cooney, M. Junge, C. Palazuelos, D. Perez-Garcia, Rank-one Quantum Games, arxiv:1112.3563 (accepted at QIP2013)
-  M. Navascues, D. Perez-Garcia, Quantum steering and space-like separation, Phys. Rev. Lett. 109, 160405 (2012)
-  T. Cooney, M. Junge, M. Navascues, D. Perez-Garcia, I. Villanueva, Joint system quantum descriptions arising from local quantumness, arxiv:1205.4110 (t.b.p. in Commun. Math. Phys.)
-  T. B. Wahl, D. Perez-Garcia, J.I. Cirac, Matrix Product States with long-range Localizable Entanglement, Phys. Rev. A A 86, 062314 (2012)
-  M. Schwarz, T.S. Cubitt, K. Temme, F. Verstraete, D. Perez-Garcia, Preparing topological PEPS on a quantum computer, arxiv:1211.4050
-  Mario Berta, Fernando Brandao, Matthias Christandl, Stephanie Wehner, Entanglement Cost of Quantum Channels, arXiv:1108.5357 (submitted to IEEE Trans. Inf. Th.)
-  Arne Hansen, Swapping Bound Entanglement, Master thesis, ETH 2012
-  Fernando Brandao and Michal Horodecki, Exponential Decay of correlations implies area law, arXiv:1206.2947
-  Ivan Kukuljan, Quantum Circuit Decompositions of Unitary Operators, State Preparation Protocols and Isometries, Semester thesis ETH (2012)
-  Alexander Müller-Hermes, David Reeb, Michael M. Wolf, Quantum Subdivision Capacities and Continuous-time Quantum Coding, arXiv:1310.2856.
-  David Reeb, Daniel Reitzner, Michael M. Wolf, Coexistence does not imply joint measurability, arXiv:1307.6986.
-  Peter Vrana, David Reeb, Daniel Reitzner, Michael M. Wolf, Fault-ignorant Quantum Search, arXiv:1307.0771.
-  David Reeb, Michael M. Wolf, (Im-)Proving Landauer's Principle, arXiv:1306.4352.
-  David Reeb, Michael M. Wolf, Tight bound on relative entropy by entropy difference, arXiv:1304.0036.
-  Benoit Collins, Motohisa Fukuda, Ion Nechita, On the convergence of output sets of quantum channels, arXiv:1311.7571.
-  Motohisa Fukuda, Revisiting additivity violation of quantum channels, arXiv:1307.0707.
-  Martin Idel, On the structure of positive maps, Master-Arbeit, LMU 2013
-  M. Berta, M. Christandl, F. Furrer, V.B. Scholz, M. Tomamichel, Continuous Variable Entropic Uncertainty Relations in the Presence of Quantum Memory, preprint arXiv:1308.4527 [quant-ph]
-  J.M. Renes, V.B. Scholz, Operationally-Motivated Uncertainty Relations for Joint Measurability and the Error-Disturbance Tradeoff, manuscript available upon request
-  M.Berta, O.Fawzi, V.B. Scholz, O.Szehr, Variations on Classical and Quantum Extractors, submitted to the IEEE International Symposium on Information Theory (2014)
-  R. Iten, Quantum Circuit Decomposition of Isometries, Semester Project (supervised by M. Christandl and R. Colbeck), publication in preparation (joint with I. Kukuljan and J. Home)
-  Marco Tomamichel, Jesus Martinez-Mateo, Christoph Pacher, David Elkouss. Fundamental Finite Key Limits for Information Reconciliation in Quantum Key Distribution (arXiv:1401.5194).
-  Gemma De las Cuevas, Norbert Schuch, David Pérez-García, J. Ignacio Cirac. Purifications of multipartite states: limitations and constructive methods. New J. Phys. 15, 123021 (2013).
-  J. Juenemann, A. Cadarso, D. Perez-Garcia, A. Bermudez, J. J. Garcia-Ripoll. Lieb-Robinson bounds for spin-boson lattice models and trapped ions. Phys. Rev. Lett. 111, 230404 (2013).
-  Toby S. Cubitt, Angelo Lucia, Spyridon Michalakis, David Perez-Garcia. Stability of local quantum dissipative systems (arXiv:1303.4744).
-  Norbert Schuch, Didier Poilblanc, J. Ignacio Cirac, David Perez-Garcia. Topological order in PEPS: Transfer operator and boundary Hamiltonians. Phys. Rev. Lett. 111, 090501 (2013).
-  J. I. Cirac, S. Michalakis, D. Perez-Garcia, N. Schuch. Robustness in Projected Entangled Pair States. Phys. Rev. B 88, 115108 (2013).
-  Marius Junge, Carlos palazuelos. Channel capacities via $p$-summing norms (arXiv:1305.1020).
-  David Elkouss, Jesus Martinez-Mateo, Vicente Martin. Analysis of a rate-adaptive reconciliation protocol and the effect of the leakage on the secret key rate. Physical Review A 87, 042334 (2013).
-  Miguel Navascues, David Perez-Garcia, Ignacio Villanueva. Testing microscopic discretization. J. Phys. A: Math. Theor. 46, 085304 (2013).
-  Martin Schwarz, Toby S. Cubitt, Kristan Temme, Frank Verstraete, David Perez-Garcia. Preparing topological PEPS on a quantum computer. Phys. Rev. A 88, 032321 (2013).