We have investigated the quantum phase transition employing the quantum renormalization-group method while, in most of the previous literature, entanglement (concurrence) has been barely demonstrated. However, it is now well known that entanglement is not the only signature of quantum correlations and a variety of computable measures have been developed to characterize quantum correlations in the composite systems. As an illustration, two cases are elaborated: a one-dimensional anisotropic (i) $XXZ$ model and (ii) an $XY$ model, with various measures of quantum correlations, including quantum discord, geometric discord, measurement-induced disturbance, measurement-induced nonlocality, and violation of Bell inequalities [e.g., Clauser-Horne-Shimony-Holt (CHSH) inequality]. We have proved that all of these correlation measures can effectively detect the quantum critical points associated with quantum phase transitions after several iterations of the renormalization in both cases. Nonetheless, it is shown that some of their dynamical behaviors are not totally similar with entanglement and, even when concurrence vanishes, there still exists some kind of quantum correlation which is not captured by entanglement. Intriguingly, CHSH inequality can never be violated in the whole iteration procedure, which indicates that block-block entanglement cannot revealed by the CHSH inequality. Moreover, the nonanalytic and scaling behaviors of Bell violation have also been discussed in detail. As a by-product, we verify that measurement-induced disturbance is exactly equal to the quantum discord measured by ${\ensuremath{\sigma}}_{z}$ for general $\mathsf{X}$ -structured states.We have investigated the quantum phase transition employing the quantum renormalization-group method while, in most of the previous literature, entanglement (concurrence) has been barely demonstrated. However, it is now well known that entanglement is not the only signature of quantum correlations and a variety of computable measures have been developed to characterize quantum correlations in the composite systems. As an illustration, two cases are elaborated: a one-dimensional anisotropic (i) $XXZ$ model and (ii) an $XY$ model, with various measures of quantum correlations, including quantum discord, geometric discord, measurement-induced disturbance, measurement-induced nonlocality, and violation of Bell inequalities [e.g., Clauser-Horne-Shimony-Holt (CHSH) inequality]. We have proved that all of these correlation measures can effectively detect the quantum critical points associated with quantum phase transitions after several iterations of the renormalization in both cases. Nonetheless, it is shown that some of their dynamical behaviors are not totally similar with entanglement and, even when concurrence vanishes, there still exists some kind of quantum correlation which is not captured by entanglement. Intriguingly, CHSH inequality can never be violated in the whole iteration procedure, which indicates that block-block entanglement cannot revealed by the CHSH inequality. Moreover, the nonanalytic and scaling behaviors of Bell violation have also been discussed in detail. As a by-product, we verify that measurement-induced disturbance is exactly equal to the quantum discord measured by ${\ensuremath{\sigma}}_{z}$ for general $\mathsf{X}$-structured states.

arXiv:1206.1202Physical Review AOct 3, 201274 citations

Numerical approach to the Bell-Clauser-Horne-Shimony-Holt inequality in quantum field theory

Philipe De Fabritiis, M. S. Guimarães, I. Roditi +1 more

The Bell-CHSH (Clauser-Horne-Shimony-Holt) inequality in the vacuum state of a relativistic scalar quantum field is analyzed. Using Weyl operators built with smeared fields localized in the Rindler wedges, the Bell-CHSH inequality is expressed in terms of the Lorentz invariant inner products of test functions. A numerical framework for these inner products is devised. Causality is also explicitly checked by a numerical evaluation of the Pauli-Jordan function. Violations of the Bell-CHSH inequality are reported for different values of the particle mass parameter. Published by the American Physical Society 2024The Bell-CHSH (Clauser-Horne-Shimony-Holt) inequality in the vacuum state of a relativistic scalar quantum field is analyzed. Using Weyl operators built with smeared fields localized in the Rindler wedges, the Bell-CHSH inequality is expressed in terms of the Lorentz invariant inner products of test functions. A numerical framework for these inner products is devised. Causality is also explicitly checked by a numerical evaluation of the Pauli-Jordan function. Violations of the Bell-CHSH inequality are reported for different values of the particle mass parameter. Published by the American Physical Society 2024

arXiv:2406.20033Physical review. D/Physical review. D.Sep 9, 20249 citations

Phase Transitions in Quantum Systems

WORLD SCIENTIFIC eBooksNov 1, 20130 citations

Phase Transitions in Quantum Systems

WORLD SCIENTIFIC eBooksAug 1, 20040 citations

An improved Bell-CHSH observable for gauge boson pairs

R. P. Grabarczyk

For particles decaying without parity violation, it is impossible to reconstruct the full spin-density matrix from the velocities of their decay products. In this work, we consider Bell inequalities based on squares of spin operators. The corresponding Bell operators probe only the part of the density matrix that can be reconstructed from any gauge boson decay or splitting to fermions, which is accessible regardless of whether parity is violated. We find that our new choice of Bell operator has promising properties regarding states seen at colliders. In particular, it substantially outperforms the inequality previously used for the $pp \rightarrow ZZ$ process at the LHC in terms of the phase space volume in which it is violated. We also conduct the first investigation of Bell violation in a system involving gauge bosons mediating different interactions, namely the $W$ boson and gluon in the $pp \rightarrow W^{\pm} (g\rightarrow b\bar{b})$ process.For particles decaying without parity violation, it is impossible to reconstruct the full spin-density matrix from the velocities of their decay products. In this work, we consider Bell inequalities based on squares of spin operators. The corresponding Bell operators probe only the part of the density matrix that can be reconstructed from any gauge boson decay or splitting to fermions, which is accessible regardless of whether parity is violated. We find that our new choice of Bell operator has promising properties regarding states seen at colliders. In particular, it substantially outperforms the inequality previously used for the $pp \rightarrow ZZ$ process at the LHC in terms of the phase space volume in which it is violated. We also conduct the first investigation of Bell violation in a system involving gauge bosons mediating different interactions, namely the $W$ boson and gluon in the $pp \rightarrow W^{\pm} (g\rightarrow b\bar{b})$ process.

arXiv:2410.18022Oct 23, 20241 citation

XXZ

model and (ii) an

XY

model, with various measures of quantum correlations, including quantum discord, geometric discord, measurement-induced disturbance, measurement-induced nonlocality, and violation of Bell inequalities [e.g., Clauser-Horne-Shimony-Holt (CHSH) inequality]. We have proved that all of these correlation measures can effectively detect the quantum critical points associated with quantum phase transitions after several iterations of the renormalization in both cases. Nonetheless, it is shown that some of their dynamical behaviors are not totally similar with entanglement and, even when concurrence vanishes, there still exists some kind of quantum correlation which is not captured by entanglement. Intriguingly, CHSH inequality can never be violated in the whole iteration procedure, which indicates that block-block entanglement cannot revealed by the CHSH inequality. Moreover, the nonanalytic and scaling behaviors of Bell violation have also been discussed in detail. As a by-product, we verify that measurement-induced disturbance is exactly equal to the quantum discord measured by ${\ensuremath{\sigma}}_{z}$ for general

\mathsf{X}

-structured states.

pp \rightarrow ZZ

process at the LHC in terms of the phase space volume in which it is violated. We also conduct the first investigation of Bell violation in a system involving gauge bosons mediating different interactions, namely the

W

boson and gluon in the

pp \rightarrow W^{\pm} (g\rightarrow b\bar{b})

process.