Description:

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Data set supporting the content of the article "Generation of scalable many-body Bell correlations in spin chains with short-range two-body interactions" by

Marcin 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:

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1) Marcin Płodzień

ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain

2) Tomasz Wasak

Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudzi ̧adzka 5, 87-100 Toruń, Poland

3) Emilia Witkowska

Institute of Physics PAS, Aleja Lotnikow 32/46, 02-668 Warszawa, Poland

4) Maciej Lewenstein

ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain

ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain

5) Jan Chwedeńczuk

Faculty of Physics, University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland

Keywords:

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nonlocality

Bell correlations

quantum spins

spin chains

ising model

finite range interactions

dynamical protocol

Directories:

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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 manuscript

data_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:

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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.dat

describes 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.dat

or

Q_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.dat

describes 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 tau

column 2 -----> value of estimated Q_N

column 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 tau

column 2 -----> value of Q_N

License:

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CC0