Abstract
We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The
k
-th condition involves comparing moments of the partially transposed ...density operator up to order
k
. Remarkably, the union of all moment inequalities reproduces the Peres-Horodecki criterion for detecting entanglement. Our empirical studies highlight that the first four conditions already detect mixed state entanglement reliably in a variety of quantum architectures. Exploiting symmetries can help to further improve their detection capabilities. We also show how to estimate moment inequalities based on local random measurements of single state copies (classical shadows) and derive statistically sound confidence intervals as a function of the number of performed measurements. Our analysis includes the experimentally relevant situation of drifting sources, i.e. non-identical, but independent, state copies.
The time evolution of the entanglement entropy is a key concept to understand the structure of a nonequilibrium quantum state. In a large class of models, such evolution can be understood in terms of ...a semiclassical picture of moving quasiparticles spreading the entanglement throughout the system. However, it is not yet known how the entanglement splits between the sectors of an internal local symmetry of a quantum many-body system. Here, guided by the examples of conformal field theories and free-fermion chains, we show that the quasiparticle picture can be adapted to this goal, leading to a general conjecture for the charged entropies whose Fourier transform gives the desired symmetry-resolved entanglement Sn (q). We point out two physically relevant effects that should be easily observed in atomic experiments: a delay time for the onset of Sn (q) which grows linearly with | Δq | (the difference between the charge q and its mean value) and an effective equipartition when | Δq | is much smaller than the subsystem size.
Rényi entropies are conceptually valuable and experimentally relevant generalizations of the celebrated von Neumann entanglement entropy. After a quantum quench in a clean quantum many-body system ...they generically display a universal linear growth in time followed by saturation. While a finite subsystem is essentially at local equilibrium when the entanglement saturates, it is genuinely out of equilibrium in the growth phase. In particular, the slope of the growth carries vital information on the nature of the system’s dynamics, and its characterization is a key objective of current research. Here we show that the slope of Rényi entropies can be determined by means of a spacetime duality transformation. In essence, we argue that the slope coincides with the stationary density of entropy of the model obtained by exchanging the roles of space and time. Therefore, very surprisingly, the slope of the entanglement is expressed as an equilibrium quantity. We use this observation to find an explicit exact formula for the slope of Rényi entropies in all integrable models treatable by thermodynamic Bethe ansatz and evolving from integrable initial states. Interestingly, this formula can be understood in terms of a quasiparticle picture only in the von Neumann limit.
A
bstract
We investigate the ground state of a (1+1)-dimensional conformal field theory (CFT) built with
M
species of massless free Dirac fermions coupled at one boundary point via a conformal ...junction/interface. Each CFT represents a wire of finite length
L
. We develop a systematic strategy to compute the Rényi entropies for a generic bipartition between the wires and the entanglement negativity between two non-complementary sets of wires. Both these entanglement measures turn out to grow logarithmically with
L
with an exactly calculated universal prefactor depending on the details of the junction and of the bipartition. These analytic predictions are tested numerically for junctions of free Fermi gases, finding perfect agreement.
A
bstract
We study the multi-charged moments for two disjoint intervals in the ground state of two 1 + 1 dimensional CFTs with central charge
c
= 1 and global U(1) symmetry: the massless Dirac field ...theory and the compact boson (Luttinger liquid). For this purpose, we compute the partition function on the higher genus Riemann surface arising from the replica method in the presence of background magnetic fluxes between the sheets of the surface. We consider the general situation in which the fluxes generate different twisted boundary conditions at each branch point. The obtained multi-charged moments allow us to derive the symmetry resolution of the Rényi entanglement entropies and the mutual information for non complementary bipartitions. We check our findings against exact numerical results for the tight-binding model, which is a lattice realisation of the massless Dirac theory.
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