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

2013
*
Physical Review Letters
*

A

doi:10.1103/physrevlett.111.080503
pmid:24010422
fatcat:rxk3sfbpdjalbfm2sry35irixq
*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 ...##
###
Identifying quantum topological phases through statistical correlation

2011
*
Physical Review B
*

We theoretically examine

doi:10.1103/physrevb.83.115119
fatcat:auwy4we7mjd2tdky24jul3disi
*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. ...##
###
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

2011
*
Physics
*

Researchers finally prove

doi:10.1103/physics.4.10
fatcat:cgdijiwmbraqzexry3nkuyz4ma
*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. ...##
###
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

2017
*
Journal of Statistical Mechanics: Theory and Experiment
*

These bounds are tighter than can be achieved using known

doi:10.1088/1742-5468/aa7ee2
fatcat:3rudcgmcivgr7owy2jsgrrcgde
*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. ...##
###
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]

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. ...

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

2009
*
Annals of Pure and Applied Logic
*

with

doi:10.1016/j.apal.2009.07.009
fatcat:qzhzh7zasvdf3gapcsvhsufloy
*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 ...##
###
Finite Correlation Length Implies Efficient Preparation of Quantum Thermal States

2018
*
Communications in Mathematical Physics
*

We require both

doi:10.1007/s00220-018-3150-8
fatcat:y5pm626lqjduvduidxaydscdsm
*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. ...##
###
Applying Rough Set Theory on DNA Recombination

2017
*
Delta Journal of Science
*

We construct a new recombination

doi:10.21608/djs.2017.139428
fatcat:xtcaxgut45bclcvkopwnibl56m
*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. ...##
###
Torsion in Cohomology Groups of Configuration Spaces

2017
*
Acta Physica Polonica. A
*

Recently, it was shown that particles constrained to move on a graph can exhibit even more exotic forms

doi:10.12693/aphyspola.132.1695
fatcat:dejm3mawrzaj5hkjbecxhn5cay
*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. ...##
###
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]

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] . ...

##
###
Quantum manifolds with classical limit
[article]

2008
*
arXiv
*
pre-print

We propose a mathematical model

arXiv:0809.3111v1
fatcat:ade72fcnvfdajc3msslgr67uwq
*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. ...
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