Datasets for "Generation of scalable many-body Bell correlations in spin chains with short-range two-body interactions"

Description:============Data set supporting the content of the article "Generation of scalable many-body Bell correlations in spin chains with short-range two-body interactions" byMarcin Płodzień, Tomasz Wasak, Emilia Witkowska, Maciej Lewenstein and Jan Chwedeńczuk.The research data consists of the data for the dynamics of the correlator as a function of time, interaction range, number of spins in the chain.The datasets also contain the research data for the dynamics of the estimated many-body Bell correlator reconstructed from the classical shadows tomography.Authors:========1) Marcin Płodzień ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain2) Tomasz WasakInstitute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudzi ̧adzka 5, 87-100 Toruń, Poland3) Emilia Witkowska Institute of Physics PAS, Aleja Lotnikow 32/46, 02-668 Warszawa, Poland4) Maciej LewensteinICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, SpainICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain5) Jan ChwedeńczukFaculty of Physics, University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, PolandKeywords:=========nonlocalityBell correlationsquantum spinsspin chainsising modelfinite range interactionsdynamical protocolDirectories:============data_correlator/epsilon_th_N_r/ - the value (right column) of the correlator E_N, see Eq. (4) of the manuscript, as a function of time tau (left column) data_correlator/Q_th_N_r/    - the value (right column) of the correlator Q_N, see Eq. (5) of the manuscript, as a function of time tau (left column)data_classical_shadows/           - datasets needed for Fig. 4 of the manuscriptdata_classical_shadows/exact_QN_N_*_r_*.txt - the value (second column) of the exact correlator Q_N calculated for given N (first *) and for given r (second *) as a function of time tau (first column), eg., exact_QN_N_4_r_3.txt is for N=4 and r=3.data_classical_shadows/est_QN_N_*_r_*.txt - the value of the estimated correlator Q_N (second column) calculated for given N (first *) and for given r (second *) as a function of time tau (first column), eg., est_QN_N_4_r_3.txt is for N=4 and r=3.Format of the data:===================1) In the directory: data_correlator/epsilon_th_N_r/*The files are of the form:epsilon_th_N.xxx_r.yyy.dat,where N=xxx is the number of spins in the spin chain and r=yyy is the range of the interaction between the spins.For example, the file epsilon_th_N.014_r.010.datdescribes N=14 spins and the interaction range is r=10. See the manuscript for the definition of r and N.2) In the directory: Q_th_N_r/*The files are of the form:_Q_th_N.xxx_r.yyy.datorQ_th_N.xxx_r.yyy.dat,where N=xxx is the number of spins in the spin chain and r=yyy is the range of the interaction between the spins.  For example, the file _Q_th_N.032_r.006.datdescribes N=32 spins and the interaction range is r=6. See the manuscript for the definition of r and N.3) In the directory: data_classical_shadows/Files in the format:data_classical_shadows/est_QN_N_*_r_*.txt, where first * stands for N and second for r, eg. est_QN_N_10_r_4.txt N=10 and r=4:column 1 -----> time taucolumn 2 -----> value of estimated Q_Ncolumn 3 -----> standard deviation of estimated Q_N (shaded region in Fig. 4).Files in the format:data_classical_shadows/exact_QN_N_*_r_*.txt, where first * stands for N and second for r, eg. exact_QN_N_8_r_4.txt N=8 and r=4:column 1 -----> time taucolumn 2 -----> value of Q_NLicense:========CC0