Entanglement Estimation in Tensor Network States via Sampling

We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction density matrix, which is highly demanding, or contraction replicas, requires an effort exponential number replicas and costly terms memory. In contrast, our stochastic sampling matrix elements classically represented reduced with respect to random drawn from simple product probability constituting frames. Even though not corresponding physical operations, such are straightforward calculate states, their moments provide Rényi entropies negativities as well symmetry-resolved components. test on one-dimensional critical XX chain two-dimensional toric code checkerboard geometry. Although cost subsystem size, it sufficiently moderate so that—in contrast other approaches—accurate results can be obtained personal computer relatively large sizes.4 MoreReceived 21 March 2022Accepted 15 June 2022DOI:https://doi.org/10.1103/PRXQuantum.3.030312Published by American Physical Society under Creative Commons Attribution 4.0 International license. Further distribution this work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement detectionEntanglement measuresQuantum information theoryTechniquesProjected entangled pair statesReplica methodsTensor methodsQuantum InformationCondensed Matter, Materials & Applied Physics