Coherence, entanglement, and quantumness in closed and open systems with conserved charge, with an application to many-body localization

Abstract

While the scaling of entanglement in a quantum system can be used to distinguish many-body quantum phases, it is usually hard to quantify the amount of entanglement in mixed states of open quantum systems, while measuring entanglement experimentally, even for the closed systems, requires in general quantum state tomography. In this work we show how to remedy this situation in system with a fixed or conserved charge, e.g., density or magnetization, due to an emerging relation between quantum correlations and coherence. First, we show how, in these cases, the presence of multipartite entanglement or quantumness can be faithfully witnessed simply by detecting coherence in the quantum system, while bipartite entanglement or bipartite quantum discord are implied by asymmetry (block coherence) in the system. Second, we prove that the relation between quantum correlations and coherence is also quantitative. Namely, we establish upper and lower bounds on the amount of multipartite and bipartite entanglement in a many-body system with a fixed local charge, in terms of the amount of coherence and asymmetry present in the system. Importantly, both for pure and mixed quantum states, these bounds are expressed as closed formulas, and furthermore, for bipartite entanglement, are experimentally accessible by means of the multiple quantum coherence spectra. In particular, in one-dimensional systems, our bounds may detect breaking of the area law of entanglement entropy. We illustrate our results on the example of a many-body localized system, also in the presence of dephasing.

Symmetric inseparability and number entanglement in charge conserving mixed states

“…1(a). This result was previously discussed 17 and here we provide a simpler derivation. As our main result, in the general case with fluctuating number of particles, we show that whenever ∆S m > 0, there exists some total charge-N block in the density matrix which is inseparable and has finite negativity, see Fig.…”

“…Its measurement protocol will be discussed in a separate publication. As a basis for this, the present work provides connections of ∆S m to results of the quantum information literature emphasizing its relationship with entanglement 17 and provides further insights why ∆S m an ideal measure of quantum entanglement in mixed states.…”

“…where ρ m = ∑ N A Π(N A )ρΠ(N A ), S(ρ) = −Tr(ρ log ρ), and Π(N A ) is a projector to a fixed number N A of the subsystem. Equivalently, ∆S m = S(ρ ρ m ) is the relative entropy of coherence with respect to N A 17 , for which a number of results have been derived 17 .…”

Characterizing the many-body localization transition by the dynamics of diagonal entropy

“…Recent developments of quantum simulation based on ultracold atoms [5][6][7][8][9], trapped ions [10], and superconduction circuits [11][12][13][14] with small coupling to thermal environment pave the way for studying MBL in large-scale systems beyond classical exact diagonalization calculations. Several characteristic dynamical properties of MBL, such as the logarithmic spreading of entanglement entropy (EE) [11,[15][16][17][18][19][20] and quantum Fisher information [10,21,22], and the power-law decay of imbalance [5][6][7][8][23][24][25][26], are observed.…”

Sharp entanglement thresholds in the logarithmic negativity of disjoint blocks in the transverse-field Ising chain

“…Entanglement plays a central role in quantum many-body theory. Exotic quantum phases such as spin liquids [1,2], topological [3,4], or many-body localized systems [5][6][7][8] find their characterization in their entanglement properties. Moreover, quantum phase transitions are signaled by a universal entanglement contribution determined solely by the universality class of the transition [9][10][11][12][13][14].…”