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Long-Range Entanglement Is Necessary for a Topological Storage of Quantum Information

Isaac H. Kim
2013 Physical Review Letters  
A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum  ...  As an example, we show that N ≤ 2γ for a large class of topologically ordered systems on a torus, where N is the number of topologically protected states and γ is the constant subcorrection term of the  ...  A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum  ... 
doi:10.1103/physrevlett.111.080503 pmid:24010422 fatcat:rxk3sfbpdjalbfm2sry35irixq

Identifying quantum topological phases through statistical correlation

Hao Wang, B. Bauer, M. Troyer, V. W. Scarola
2011 Physical Review B  
We theoretically examine the use of a statistical distance measure, the indistinguishability, as a generic tool for the identification of topological order.  ...  Calculations with the indistinguishability also underscore a key distinction between symmetries that underlie topological order in the toric code and quantum Hall models.  ...  We have thus shown that the indistinguishability reveals the size of the operators required to identify topological sectors.  ... 
doi:10.1103/physrevb.83.115119 fatcat:auwy4we7mjd2tdky24jul3disi

Page 1036 of Mathematical Reviews Vol. , Issue 87b [page]

1987 Mathematical Reviews  
(D-MUNS-TP) 87b:81005 On the quantum properties of indistinguishable classical particles. Lett. Nuovo Cimento (2) 43 (1985), no. 8, 383-387.  ...  is the corresponding density operator, M a sub- set of the space of its possible phase-space trajectories, and F(-) and Piw,+,) are an effect-valued measure (EVM) and a probability measure on the trajectory  ... 

A landmark proof

Frank Wilczek
2011 Physics  
Researchers finally prove the conjecture that the low-energy excitations of some quantum Hall states are non-Abelian anyons.  ...  He has been Professor of physics at Princeton University, Robert Huttenback Professor of physics and member of the Institute for Theoretical Physics at the University of California, Santa Barbara, and  ...  About the Author Frank Wilczek Frank Wilczek is Herman Feshbach Professor of physics in the Center for Theoretical Physics at MIT.  ... 
doi:10.1103/physics.4.10 fatcat:cgdijiwmbraqzexry3nkuyz4ma

Page 3476 of Mathematical Reviews Vol. , Issue 89F [page]

1989 Mathematical Reviews  
This paper analyzes a special class of indistinguishable classical particles that has been introduced by Brillouin and which general- izes the usual Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics  ...  In the context of the ideas indicated above, we place each interaction in correspondence with a certain class of topological spaces, and compare it to a numer- ical code, based on which we construct the  ... 

Topological quantum error correction in the Kitaev honeycomb model

Yi-Chan Lee, Courtney G Brell, Steven T Flammia
2017 Journal of Statistical Mechanics: Theory and Experiment  
These bounds are tighter than can be achieved using known general properties of topological phases.  ...  The appearance of non-topological excitations in this setting has no significant effect on the error correction properties of the honeycomb model in the regimes we study.  ...  We will call the K α q link generators to distinguish them from the more general class of link operators that they generate under multiplication.  ... 
doi:10.1088/1742-5468/aa7ee2 fatcat:3rudcgmcivgr7owy2jsgrrcgde

Page 1149 of Mathematical Reviews Vol. , Issue 87c [page]

1987 Mathematical Reviews  
The links between F- indistinguishability operators and a class of generalized metrics in the unit interval—which are also explored—are used to define the canonical generators of an F-indistinguishability  ...  Author summary: “Some properties concerning the structure of F-indistinguishability operators are analyzed. It is shown that any such operator is generated by a family of fuzzy subsets.  ... 

Borel quantization and nonlinear quantum mechanics. A review of developments in the series "Symmetries in Science" I - XIII [article]

H.-D. Doebner, J. Tolar
2006 arXiv   pre-print
The results, different aspects and applications of our method of quantisation on configuration manifolds - called Borel Quantisation - were presented at meetings of the series 'Symmetries in Science' and  ...  The developments with numerous coauthors, on Borel quantisation and the related family of nonlinear Schr\"odinger equations called Doebner-Goldin equations, are reviewed and commented here.  ...  Acknowledgements One of the authors (HDD) acknowledges discussions with Alois Kopp.  ... 
arXiv:quant-ph/0601176v1 fatcat:3ofyhjdyk5bcrcrcxdqlso32te

On intuitionistic modal and tense logics and their classical companion logics: Topological semantics and bisimulations

J.M. Davoren
2009 Annals of Pure and Applied Logic  
with an equivalence relation R with the property that the R-expansion of an open set is open.  ...  characterizes a Hennessy-Milner class of topological models between any pair of which there is a maximal topological bisimulation that preserve the intuitionistic semantics.  ...  of models have the Hennessy-Milner property that indistinguishability under a topological bisimulation coincides with indistinguishability in the intuitionistic logic, or with indistinguishability in  ... 
doi:10.1016/j.apal.2009.07.009 fatcat:qzhzh7zasvdf3gapcsvhsufloy

Finite Correlation Length Implies Efficient Preparation of Quantum Thermal States

Fernando G. S. L. Brandão, Michael J. Kastoryano
2018 Communications in Mathematical Physics  
We require both properties to hold for the thermal state of the Hamiltonian on any induced subgraph of the original lattice.  ...  properties: (i) the correlations between two regions are exponentially decaying in the distance between the regions, and (ii) the thermal state is an approximate Markov state for shielded regions.  ...  We thank Isaac Kim for pointing out the unpublished result of Kitaev to us. MJK was supported by the Carlsberg fund and the Villum fund.  ... 
doi:10.1007/s00220-018-3150-8 fatcat:y5pm626lqjduvduidxaydscdsm

Applying Rough Set Theory on DNA Recombination

M. M. Elsharkasy, M. Sh. Badr, Wafaa M. Fouda
2017 Delta Journal of Science  
We construct a new recombination operator using the properties of DNA and RNA.  ...  Using the process of cutting and sticking of a sequence of genes, new types of topological structures are constructed and some of their properties and characterization are investigated.  ...  We constructed two new recombination operators using the properties of DNA and RNA. We study topological properties of the constructed operators and the associated topological spaces of DNA and RNA.  ... 
doi:10.21608/djs.2017.139428 fatcat:xtcaxgut45bclcvkopwnibl56m

Torsion in Cohomology Groups of Configuration Spaces

T. Maciążek, A. Sawicki
2017 Acta Physica Polonica. A  
Recently, it was shown that particles constrained to move on a graph can exhibit even more exotic forms of quantum statistics, depending on the topology of the graph.  ...  An important and surprising discovery in physics in the last fifty years is that if quantum particles are constrained to move in two rather than three dimensions, they can in principle exhibit new forms  ...  Of particular importance for the description of quantum statistics for indistinguishable particles is topology of the underlying configuration space.  ... 
doi:10.12693/aphyspola.132.1695 fatcat:dejm3mawrzaj5hkjbecxhn5cay

Page 4882 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews  
Summary: “We consider two situations which relate properties of filters to properties of the limit operators with respect to these fil- ters.  ...  Miiller’s results (some of which may have never ap- peared before), and the Marinescu modifier, which generates the coreflective hull of the category of abelian topological groups in the category of abelian  ... 

Descriptive Proximities I: Properties and interplay between classical proximities and overlap [article]

A. Di Concilio, C. Guadagni, J.F. Peters, S. Ramanna
2016 arXiv   pre-print
The theory of descriptive nearness is usually adopted when dealing with sets that share some common properties even when the sets are not spatially close, i.e., the sets have no members in common.  ...  We establish a connection between relations on an object space X and relations on the feature space Φ(X).  ...  When δ is a Lodato proximity, then: Property.1 The associated closure operator cl δ is a Kuratowski operator [7, 8] .  ... 
arXiv:1609.06246v1 fatcat:xlzczxlkljgn7eaarr55tlwdxe

Quantum manifolds with classical limit [article]

Manuel Hohmann, Raffaele Punzi, Mattias N.R. Wohlfarth
2008 arXiv   pre-print
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space.  ...  In this picture we demonstrate that classical spacetime emerges as a finite-dimensional manifold through the topological identification of all quantum points with identical position expectation value.  ...  The sets X i and W i consist of equivalence classes of topologically indistinguishable elements of U i and V i , respectively.  ... 
arXiv:0809.3111v1 fatcat:ade72fcnvfdajc3msslgr67uwq
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