scholarly journals Holographic view on quantum correlations and mutual information between disjoint blocks of a quantum critical system

2011 ◽  
Vol 2011 (10) ◽  
Author(s):  
Javier Molina-Vilaplana ◽  
Pasquale Sodano
Keyword(s):  
Mutual Information ◽  
Quantum Correlations ◽  
Critical System ◽  
Quantum Critical

scholarly journals Computable Rényi mutual information: Area laws and correlations

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 541
Author(s):  
Samuel O. Scalet ◽  
Álvaro M. Alhambra ◽  
Georgios Styliaris ◽  
J. Ignacio Cirac
Keyword(s):  
Mutual Information ◽  
Correlation Functions ◽  
Quantum Correlations ◽  
Matrix Product ◽  
Many Body ◽  
Von Neumann ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States ◽  
Area Law

The mutual information is a measure of classical and quantum correlations of great interest in quantum information. It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all correlation functions. However, calculating it exactly or approximately is often challenging in practice. Here, we consider alternative definitions based on Rényi divergences. Their main advantage over their von Neumann counterpart is that they can be expressed as a variational problem whose cost function can be efficiently evaluated for families of states like matrix product operators while preserving all desirable properties of a measure of correlations. In particular, we show that they obey a thermal area law in great generality, and that they upper bound all correlation functions. We also investigate their behavior on certain tensor network states and on classical thermal distributions.

Static and dynamic susceptibility in the putative ferromagnetic quantum critical system YbNi4 P2 probed by 31 P NMR

2013 ◽  
Vol 250 (3) ◽  
pp. 519-521 ◽  
Author(s):  
Rajib Sarkar ◽  
Panchanan Khuntia ◽  
Johannes Spehling ◽  
Cornelius Krellner ◽  
Christoph Geibel ◽  
...  
Keyword(s):  
Dynamic Susceptibility ◽  
Critical System ◽  
Quantum Critical

Entropy, energy, and entanglement of localized states in bent triatomic molecules

2017 ◽  
Vol 31 (12) ◽  
pp. 1750088 ◽  
Author(s):  
Qiang Yuan ◽  
Xi-Wen Hou
Keyword(s):  
Quantum Information ◽  
Mutual Information ◽  
Quantum Correlations ◽  
Localized States ◽  
Quantum Entropy ◽  
Intramolecular Dynamics ◽  
Initial State ◽  
Triatomic Molecules ◽  
Localized State ◽  
Bending Mode

The dynamics of quantum entropy, energy, and entanglement is studied for various initial states in an important spectroscopic Hamiltonian of bent triatomic molecules H2O, D2O, and H2S. The total quantum correlation is quantified in terms of the mutual information and the entanglement by the concurrence borrowed from the theory of quantum information. The Pauli entropy and the intramolecular energy usually used in the theory of molecules are calculated to establish a possible relationship between both theories. Sections of two quantities among these four quantities are introduced to visualize such relationship. Analytic and numerical simulations demonstrate that if an initial state is taken to be the stretch- or the bend-vibrationally localized state, the mutual information, the Pauli entropy, and the concurrence are dominant-positively correlated while they are dominantly anti-correlated with the interacting energy among three anharmonic vibrational modes. In particular, such correlation is more distinct for the localized state with high excitations in the bending mode. The nice quasi-periodicity of those quantities in D2O molecule reveals that this molecule prepared in the localized state in the stretching or the bending mode can be more appreciated for molecular quantum computation. However, the dynamical correlations of those quantities behave irregularly for the dislocalized states. Moreover, the hierarchy of the mutual information and the Pauli entropy is explicitly proved. Quantum entropy and energy in every vibrational mode are investigated. Thereby, the relation between bipartite and tripartite entanglements is discussed as well. Those are useful for the understanding of quantum correlations in high-dimensional states in polyatomic molecules from quantum information and intramolecular dynamics.

scholarly journals Phase diagram of quantum critical system via local convertibility of ground state

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Si-Yuan Liu ◽  
Quan Quan ◽  
Jin-Jun Chen ◽  
Yu-Ran Zhang ◽  
Wen-Li Yang ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Ground State ◽  
Critical System ◽  
Quantum Critical

scholarly journals Hydrodynamics of quantum entropies in Ising chains with linear dissipation

2022 ◽  
Author(s):  
Vincenzo Alba ◽  
Federico Carollo
Keyword(s):  
Mutual Information ◽  
Hydrodynamic Limit ◽  
Transverse Field ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Simple Description ◽  
Von Neumann ◽  
Long Time ◽  
Dynamics Of Correlations ◽  
Quasiparticle Picture

Abstract We study the dynamics of quantum information and of quantum correlations after a quantum quench, in transverse field Ising chains subject to generic linear dissipation. As we show, in the hydrodynamic limit of long times, large system sizes, and weak dissipation, entropy-related quantities —such as the von Neumann entropy, the Rényi entropies, and the associated mutual information— admit a simple description within the so-called quasiparticle picture. Specifically, we analytically derive a hydrodynamic formula, recently conjectured for generic noninteracting systems, which allows us to demonstrate a universal feature of the dynamics of correlations in such dissipative noninteracting system. For any possible dissipation, the mutual information grows up to a time scale that is proportional to the inverse dissipation rate, and then decreases, always vanishing in the long time limit. In passing, we provide analytic formulas describing the time-dependence of arbitrary functions of the fermionic covariance matrix, in the hydrodynamic limit.

scholarly journals Identification of the low-energy excitations in a quantum critical system

AIP Advances ◽  
2016 ◽  
Vol 7 (5) ◽  
pp. 055701 ◽  
Author(s):  
Tom Heitmann ◽  
Jagat Lamsal ◽  
Shannon Watson ◽  
Ross Erwin ◽  
Wangchun Chen ◽  
...  
Keyword(s):  
Low Energy ◽  
Critical System ◽  
Quantum Critical
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