Symmetry-resolved dynamical purification in synthetic quantum matter

Abstract

When a quantum system initialized in a product state is subjected to either coherent or incoherent dynamics, the entropy of any of its connected partitions generically increases as a function of time, signalling the inevitable spreading of (quantum) information throughout the system. Here, we show that, in the presence of continuous symmetries and under ubiquitous experimental conditions, symmetry-resolved information spreading is inhibited due to the competition of coherent and incoherent dynamics: in given quantum number sectors, entropy decreases as a function of time, signalling dynamical purification. Such dynamical purification bridges between two distinct short and intermediate time regimes, characterized by a log-volume and log-area entropy law, respectively. It is generic to symmetric quantum evolution, and as such occurs for different partition geometry and topology, and classes of (local) Liouville dynamics. We then develop a protocol to measure symmetry-resolved entropies and negativities in synthetic quantum systems based on the random unitary toolbox, and demonstrate the generality of dynamical purification using experimental data from trapped ion experiments [Brydges et al., Science 364, 260 (2019)]. Our work shows that symmetry plays a key role as a magnifying glass to characterize many-body dynamics in open quantum systems, and, in particular, in noisy-intermediate scale quantum devices.

Symmetry resolved entanglement in integrable field theories via form factor bootstrap

“…Many results are also known for microscopical models on the lattice [7,[14][15][16][23][24][25][26][27][28][29][30][31], disordered systems [32][33][34], and for non-trivial topological phases [35,36]. Symmetry resolved quantities can also be measured experimentally [37]. It is worth saying that the charged moments (6) have also been the subject of field theoretical studies before their application to symmetry resolved entropies was recognised [38][39][40][41][42][43][44].…”

Entanglement Hamiltonians: from field theory, to lattice models and experiments

“…Compared to alternative methods based on implementing multiple copies to measure Rényi entropies [122][123][124][125], negativities [126], (and also the ES [108]), the protocols presented above involve single instances of the quantum states and appear thus as more experimentally friendly. Finally, protocols based on measuring statistical correlations between randomized measurements have been also devised to measure entanglement entropies [115,[127][128][129][130][131], and entanglement negativities [132,133]. These protocols have the advantage of not making assumptions on the state, and of not requiring multiple copies.…”

Symmetry-resolved entanglement entropy in critical free-fermion chains

“…Here S is the usual von Neumann entropy calculated in [37], and the derivatives γ ′ 2 (1) and γ ′ 4 (1) can be given as integrals using (17). Numerically, γ ′ 2 (1) ≃ 0.0546 and γ ′ 4 (1) ≃ 0.00154 [19,57].…”