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Entanglement – A Measure for the Complexity of Directed Graphs with Applications to Logic and Games [chapter]

Dietmar Berwanger, Erich Grädel
2005 Lecture Notes in Computer Science  
We propose a new parameter for the complexity of finite directed graphs which measures to what extent the cycles of the graph are intertwined.  ...  This measure, called entanglement, is defined by way of a game that is somewhat similar in spirit to the robber and cops games used to describe tree width, directed tree width, and hypertree width.  ...  1 Entanglement: How to catch a thief Let G = (V, E) be a finite directed graph. The entanglement of G, denoted ent(G), measures to what extent the cycles of G are entangled.  ... 
doi:10.1007/978-3-540-32275-7_15 fatcat:tl6vjbenwnb3ln2phdlkqhf5aq

Directed Graphs of Entanglement Two [chapter]

Erich Grädel, Łukasz Kaiser, Roman Rabinovich
2009 Lecture Notes in Computer Science  
Entanglement is a complexity measure for directed graphs that was used to show that the variable hierarchy of the propositional modal µ-calculus is strict.  ...  We study the general case of directed graphs of entanglement two and prove that they can be decomposed as well, in a way similar to the known decompositions for tree-width, DAG-width and Kelly-width.  ...  While tree-width indicates how closely a graph resembles a tree, the intuition behind complexity measures for directed graphs is that acyclic graphs are simple, and that we can measure the complexity of  ... 
doi:10.1007/978-3-642-03409-1_16 fatcat:qi2cdnhegjan3jcbfzcta3rldm

Closure Under Minors of Undirected Entanglement [article]

Walid Belkhir
2009 arXiv   pre-print
Entanglement is a digraph complexity measure that origins in fixed-point theory. Its purpose is to count the nested depth of cycles in digraphs.  ...  Our proof relies on the game theoretic characterization of entanglement in terms of Robber and Cops games.  ...  Introduction Entanglement is a complexity measure of finite directed graphs introduced in [5] as a tool to analyze the descriptive complexity of the propositional modal µ-calculus [6] .  ... 
arXiv:0904.1703v1 fatcat:mj6mqbnuujfu5dunxigur5bdai

Entanglement and the complexity of directed graphs

Dietmar Berwanger, Erich Grädel, Łukasz Kaiser, Roman Rabinovich
2012 Theoretical Computer Science  
Entanglement is a parameter for the complexity of finite directed graphs that measures to what extent the cycles of the graph are intertwined.  ...  We study complexity issues for entanglement and compare it to other structural parameters of directed graphs.  ...  Acknowledgments This work has been partially supported by the ESF Networking Programme GAMES.  ... 
doi:10.1016/j.tcs.2012.07.010 fatcat:cd3q3i43arcznefrbk6xmkze3a

Multi-partite entanglement [article]

Michael Walter and David Gross and Jens Eisert
2017 arXiv   pre-print
We end with a brief discussion of various applications that rely on multi-partite entangled states: quantum networks, measurement-based quantum computing, non-locality, and quantum metrology.  ...  states, stabilizer and graph states, bosonic and fermionic Gaussian states, addressing applications in condensed matter theory.  ...  A graph state is defined by a graph with one vertex for every qubit (cf. Fig. 1) .  ... 
arXiv:1612.02437v2 fatcat:yxhwwigxurc6vc6ejsa2r7vn74

On the Role of Shared Entanglement [article]

Dmitry Gavinsky
2006 arXiv   pre-print
We base the lower bounds on a strong direct product theorem for communication complexity of a certain class of relational problems.  ...  Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former.  ...  Acknowledgments I thank John Watrous and Ronald de Wolf for helpful discussions.  ... 
arXiv:quant-ph/0604052v2 fatcat:ddwt3fl5cngr5axh5crk4cy7fm

Quantum Entanglement in Time [article]

Del Rajan
2020 arXiv   pre-print
An original contribution of this thesis is the design of one of the first applications of entanglement in time.  ...  In this doctoral thesis we provide one of the first theoretical expositions on a quantum effect known as entanglement in time.  ...  Let G be a graph with a set of N vertices and certain number of edges connecting them.  ... 
arXiv:2007.05969v1 fatcat:3tcqbfuyrjavtdtdxkbszrdyke

Undirected Graphs of Entanglement 3 [article]

Walid Belkhir
2009 arXiv   pre-print
Entanglement is a complexity measure of digraphs that origins in fixed-point logics. Its combinatorial purpose is to measure the nested depth of cycles in digraphs.  ...  We address the problem of characterizing the structure of graphs of entanglement at most k. Only partial results are known so far: digraphs for k=1, and undirected graphs for k=2.  ...  . , n, contains a hinge Acknowledgement. We acknowledge Luigi Santocanale for helpful discussions on the topic.  ... 
arXiv:0904.1696v1 fatcat:q7ghlbab2rcwbh6us6eo3n4hmm

Quantum entanglement

Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, Karol Horodecki
2009 Reviews of Modern Physics  
All our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory.  ...  But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger - waited over 70 years to enter to laboratories as a new resource as real as energy.  ...  We also thank many other colleagues in the field of quantum information for discussions and useful feedback. We wish also to acknowledge the referees for their fruitful criticism.  ... 
doi:10.1103/revmodphys.81.865 fatcat:6ahjbb4iyzfn5jgsocbeodmsqm

Contextuality in entanglement-assisted one-shot classical communication [article]

Shiv Akshar Yadavalli, Ravi Kunjwal
2021 arXiv   pre-print
We then show a mapping between this communication task and a corresponding nonlocal game. This mapping generalizes the connection with pseudotelepathy games previously noted in the zero-error case.  ...  This strategy uses the Kochen-Specker theorem which is applicable only to projective measurements.  ...  Pusey for raising the issue of the role of nonlocality in the early phase of this project when some of these ideas were presented in a "Lobster Lunch" talk at Oxford.  ... 
arXiv:2006.00469v3 fatcat:fymjyrmmazg2pbo4z7moviurla

Measurement-based quantum communication with resource states generated by entanglement purification

J. Wallnöfer, W. Dür
2017 Physical Review A  
We show that such an approach offers advantages over direct transmission, gate-based error correction and measurement-based schemes with direct generation of resource states.  ...  We analyze the noise structure of resource states generated by entanglement purification and show that a local error model, i.e. noise acting independently on all qubits of the resource state, is a good  ...  ACKNOWLEDGEMENTS This work was supported by the Austrian Science Fund (FWF): P24273-N16, P28000-N27.  ... 
doi:10.1103/physreva.95.012303 fatcat:hc2tqkmbsnh2nb55sxq2lzeea4

A quantum network stack and protocols for reliable entanglement-based networks

Alexander Pirker, Wolfgang Duer
2019 New Journal of Physics  
We present a stack model for breaking down the complexity of entanglement-based quantum networks.  ...  The layers responsibilities range from establishing point-to-point connectivity, over intra-network graph state generation, to inter-network routing of entanglement.  ...  Acknowledgments This work was supported by the Austrian Science Fund (FWF): P28000-N27 and P30937-N27. We thank J Wallnöfer for helpful discussions and comments on the manuscript.  ... 
doi:10.1088/1367-2630/ab05f7 fatcat:5eivx4go6rcbpj35xakw36ymni

Quantum entanglement in topological phases on a torus

Zhu-Xi Luo, Yu-Ting Hu, Yong-Shi Wu
2016 Physical review B  
We obtain a general formula for entanglement entropy and generalize the concept of minimally entangled states to minimally entangled sectors.  ...  The cylindrical topology of the subsystems makes a significant difference in regard to entanglement: a global quantum number for the many-body states comes into play, together with a decomposition matrix  ...  Acknowledgments We thank Yang Qi for valuable comments and suggestions. Zhuxi thanks Ren Pankovich for inspiring discussions.  ... 
doi:10.1103/physrevb.94.075126 fatcat:adbkmtsyebhzhgugoeguvnp63q

A New Objective Definition of Quantum Entanglement as Potential Coding of Intensive and Effective Relations [article]

Christian de Ronde, César Massri
2019 arXiv   pre-print
In [20] it was argued against the orthodox definition of quantum entanglement in terms of pure and separable states.  ...  In this paper we attempt to discuss how the logos categorical approach to quantum mechanics [18, 19] is able to provide an objective formal account of the notion of entanglement --completely independent  ...  Acknowledgements We want to thank an anonymous referee for her/his insightful remarks and comments.  ... 
arXiv:1809.00202v2 fatcat:snix3jyvsvdsflhi2rzujmumei

Quantum Entanglement on a Hypersphere

James F. Peters, Arturo Tozzi
2016 International Journal of Theoretical Physics  
We propose an unusual history of the Universe, drawing a coherent chronology from pre-big bang scenarios to the occurence of the human brain.  ...  Our math-framed account emphasizes the explanatory role of broken symmetries and topological features in physical, biological, neuroscientific and medical events.  ...  Importantly, it opens the door to a series of new predictions and future directions of advancement for neuroscientific research.  ... 
doi:10.1007/s10773-016-2998-7 fatcat:j5iwqp4z2fglfjul4dzsbh3oru
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