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Are problems in Quantum Information Theory (un)decidable? [article]

Michael M. Wolf, Toby S. Cubitt, David Perez-Garcia
2011 arXiv   pre-print
This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice).  ...  We review some of the main tools for (dis)proving decidability and apply them to problems in quantum information theory.  ...  In the present paper we will, however, focus exclusively on problems occurring in quantum information theory. 1 Moreover, we will restrict ourselves to decidability problems and, for the moment, leave  ... 
arXiv:1111.5425v1 fatcat:tivo3fmt3new3neekoe43fs76y


Cristian S. Calude, José Félix Costa
2009 Natural Computing  
We are also indebted to Professor Grzegorz Rozenberg for publishing this group of papers in a Special Issue of the journal Natural Computing.  ...  The authors discuss the separation of the corresponding functional classes by quantum state identifications.  ...  The author shows how to use quantum measurements to test the (un)decidability of certain mathematical propositions, namely that elementary quantum systems are capable of encoding finite axioms, and quantum  ... 
doi:10.1007/s11047-009-9113-4 fatcat:7bxke4eccvastpzaddxbnrymxu

Page 2644 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews  
is un- decidable (358-369); Michael Elkin and David Peleg, The hard- ness of approximating spanner problems (370-381); Hans-Joachim Béckenhauer, Juraj Hromkovi¢, Ralf Klasing, Sebastian Seibert  ...  ISBN 3-540-66694-X The 37 papers in this collection include the following: Jozef Gruska, Quantum challenges (1-28); Juraj Hromkovit, Stabil- ity of approximation algorithms for hard optimization problems  ... 

Measurement-Based Quantum Computation and Undecidable Logic

Maarten Van den Nest, Hans J. Briegel
2008 Foundations of physics  
states--are associated with undecidable logic theories.  ...  We show that the computational power of an important class of quantum states called graph states, representing resources for measurement-based quantum computation, is reflected in the expressive power  ...  Before giving examples of (un)decidable MS theories, is important to make the following two remarks.  ... 
doi:10.1007/s10701-008-9212-6 fatcat:y5wqly4oqvbufbezfksf7kvcvq

Intrinsic and Extrinsic Observation Mode [chapter]

Karl Svozil
2018 Physical (A)Causality  
Without epistemology any inroad into the subject of (un)decidability and (in)determinism may result in confusion and incomprehensibility.  ...  I strongly suspect that this simple fact is at the root of the measurement problem in quantum theory, in which the reversible dynamical laws cannot be used to describe the measurement process.  ...  Other eminent quantum physicists like Greenberger are proclaiming that "quantum mechanics is magic."  ... 
doi:10.1007/978-3-319-70815-7_1 fatcat:bzylwybqgrexlllnghzcgvpfya

Reachability analysis of quantum Markov decision processes

Shenggang Ying, Mingsheng Ying
2018 Information and Computation  
The (un)decidability and complexity of these problems are settled, or their relationships with certain long-standing open problems are clarified.  ...  It is shown by examples that qMDPs can be used in analysis of quantum algorithms and protocols.  ...  The (un)decidability and complexity of a series of reachability problems for qMDPs were settled, but several others left unsolved (the exact complexity of Problem 3.3.1 and the general case of Problem  ... 
doi:10.1016/j.ic.2018.09.001 fatcat:6ejkh6ytanca5olypns57ygfky

Reachability Analysis of Quantum Markov Decision Processes [article]

Shenggang Ying, Mingsheng Ying
2014 arXiv   pre-print
The (un)decidability and complexity of these problems are settled, or their relationships with certain long-standing open problems are clarified.  ...  It is shown by examples that qMDPs can be used in analysis of quantum algorithms and protocols.  ...  Acknowledgments We are very grateful to Yuan Feng and Youming Qiao for helpful discussions.  ... 
arXiv:1406.6146v2 fatcat:vg7ixjpxkfbslhehyzohgllxrq

A Note on Quantum Markov Models [article]

Christino Tamon, Weichen Xie
2019 arXiv   pre-print
Given that most relevant problems related to Markov decision process are undecidable classically (which immediately implies undecidability in the quantum case), this provides one of the few examples where  ...  the quantum problem is tractable.  ...  The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of Air  ... 
arXiv:1911.01953v1 fatcat:msovcdt5cfh7tk2lqnoyws5h3e

Recent Publications

Richard A. Good, Donald A. Norton, H. Mirkil, Robert L. Stanley, Albert Newhouse, Nathan Grier Parke, D. L. Falkoff, Felix Haas, Hartley Rogers, W. Givens, Morris Newman, Howard E. Campbell (+1 others)
1960 The American mathematical monthly  
A reference to work of Tarski would have been ap- propriate here (and at some other places). (2) In connection with the “un- decidable” statement G that asserts its own unprovability, the authors state  ...  The remaining six chapters deal with selected topics in quantum mechanics including a chapter on quantum chemistry and another on the theory of a quantised field.  ... 
doi:10.1080/00029890.1960.11989453 fatcat:o4dfbdxgh5erdarrhdo3nwp6em

Quantum mechanics without interpretation [article]

O. Yaremchuk
2001 arXiv   pre-print
Quantum mechanics is one of these theories.  ...  Due to the structural inhomogeneity of the intermediate set, its complete description falls into several "sections" (theories) with their special main laws, dimensions, and directions, i.e., the complete  ...  Based only on the top view, the problem of separation (and even existence) of the black-and-white bricks of this kind is un-decidable. Each brick can be black-and-white with equal probability.  ... 
arXiv:quant-ph/0007075v4 fatcat:cxuhzi4cbjd2lbljacst6a57j4

Against the factory school of modern times: the need of a paradigmatic rupture

Jesus Maria Sousa
2021 South Florida Journal of Development  
of the modernist curriculum implemented at schools, and the real need for a global and interdisciplinary methodological approach focused on the greatest problems of humanity.  ...  A paradigm shift in the area of education and teacher education is a must.  ...  They are for instance the quantum mechanics of Max Planck (1858-1947) and the probabilistic theories, the wave mechanics of Louis de Broglie (1892-1987), the correspondence and complementarity theories  ... 
doi:10.46932/sfjdv2n2-194 fatcat:kpv2zwsb2rgufnhrpqulibs7qu

Operational quantum logic: An overview [article]

Bob Coecke, David Moore, Alexander Wilce
2001 arXiv   pre-print
The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra.  ...  Our aim here is to give a uniform presentation of what we call operational quantum logic, highlighting both its concrete physical origins and its purely mathematical structure.  ...  This sustained interest reflects in part the fact that the basic ideas and language of quantum logic inform most discussions of the vexing foundational problems of quantum mechanics (indeed, to a degree  ... 
arXiv:quant-ph/0008019v2 fatcat:d3ovzfpkx5afze6qe724mtv5te

Operational Quantum Logic: An Overview [chapter]

Bob Coecke, David Moore, Alexander Wilce
2000 Current Research in Operational Quantum Logic  
Consequently, there is a particular focus in this paper on the (survey) articles of that volume, which are dedicated to D.J.  ...  Foulis in honor of his seminal contributions to our field. 2 The author is Postdoctoral Researcher at Flanders' Fund for Scientific Reseach.  ...  This sustained interest reflects in part the fact that the basic ideas and language of quantum logic inform most discussions of the vexing foundational problems of quantum mechanics (indeed, to a degree  ... 
doi:10.1007/978-94-017-1201-9_1 fatcat:ubb4ku7xhfb5nfv6nrjm7jujza

Algorithmic Economics: Incomputability, Undecidability and Unsolvability in Economics [chapter]

K. Vela Velupillai
2017 The Incomputable  
'Why do these matters', of (in)computability, (un)decidability and (un)solvability, 'turn up', in economics, as Paul Feyerabend posed it, in his letter to me 4 .  ...  From the early 1950s Simon had empirically investigated evidence on human problem solving and had organised that evidence within an explicit framework of a theory of sequential information processing by  ... 
doi:10.1007/978-3-319-43669-2_7 fatcat:l2rlubnx6nejhl24g2i43r5wp4

Humanities-Based Assessment of Natural Scientists' Assessment of Social Science

Hajime Eto
2016 International Journal of Social Science and Humanity  
Confronting serious social issues, many natural scientists (including technologists) are dissatisfied with the performance of social science.  ...  Reflecting how the 20-th century's humanities have overcome the problem of natural scientific crises, this paper advises natural scientists to remember their own history and to consider the ethos of social  ...  , the un-decidability of the truth, validities, and other fundamental concepts of mathematics.  ... 
doi:10.18178/ijssh.2016.v6.782 fatcat:7sxa44jjxfe3riexqdp5gdjytu
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