Genuine quantum correlations in quantum many-body systems: a review of recent progress

Abstract

Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems.

Bipartite entanglement entropy of the excited states of free fermions and harmonic oscillators

“…These studies were followed with many other interesting results which paved the way to better understanding of the bipartite entanglement entropy of the ground state of the free fermions [5][6][7], coupled harmonic oscillators [8][9][10], quantum spin chains [11][12][13], CFTs [14] and topological systems [15,16]. To review various applications of the bipartite entanglement entropy of the ground state in many-body quantum systems and quantum field theories see [17][18][19][20][21][22][23][24] and [25][26][27] respectively. Although the investigation of the bipartite entanglement entropy of the ground state of quantum systems has a long history the same is not true for the excited states.…”

Scaling of decoherence and energy flow in interacting quantum spin systems

“…The approach to such an asymptotic behavior is characterized by power-law corrections, typically controlled by irrelevant perturbations at the corresponding fixed point [37]. The equilibrium FSS at quantum transitions has been also extended to quantuminformation concepts [61][62][63][64][65], such as the ground-state fidelity and its susceptibility, which measure the change of the ground state when varying the Hamiltonian parameters around a quantum transition [50].…”

Enhancing violations of Leggett-Garg inequalities in nonequilibrium correlated many-body systems by interactions and decoherence

“…After gathering the coefficients a m,n of all the different basis elements |K − m K − n| in Eqs. (S11) and (S13), and considering that a * m,n = a n,m so the density matrix is Hermitian, we obtain a linear system of equations whose solution gives the correctionρ (1) . Rewriting each correction coefficient as a m,n = r m,n + ij m,n and considering the Hermiticity of the density matrix (r m,n = r n,m and j m,n = −j n,m ), this is transformed into a linear system of 1 + K 2 equations with (K 2 + K + 2)/2 unknowns r m,n (including r s ≡ a s ) and (K 2 − K)/2 unknowns j m,n (the diagonal elements must be real).…”