Nonstabilizerness versus entanglement in matrix product states

Year: 2024

Authors: Frau M., Tarabunga PS., Collura M., Dalmonte M., Tirrito E.

Autors Affiliation: Int Sch Adv Studies SISSA, Via Bonomea 265, I-34136 Trieste, Italy; Abdus Salam Int Ctr Theoret Phys ICTP, Str Costiera 11, I-34151 Trieste, Italy; INFN, Sez Trieste, Via Valerio 2, I-34127 Trieste, Italy; Univ Trento, Pitaevskii BEC Ctr, CNR INO, Via Sommar 14, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, Via Sommar 14, I-38123 Trento, Italy.

Abstract: In this paper, we investigate the relationship between entanglement and nonstabilizerness (also known as magic) in matrix product states (MPSs). We study the relation between magic and the bond dimension used to approximate the ground state of a many-body system in two different contexts: full state of magic and mutual magic (the nonstabilizer analog of mutual information, thus free of boundary effects) of spin-1 anisotropic Heisenberg chains. Our results indicate that obtaining converged results for nonstabilizerness is typically considerably easier than entanglement. For full state magic at critical points and at sufficiently large volumes, we observe convergence with 1/x2, with x being the MPS bond dimension. At small volumes, magic saturation is so quick that, within error bars, we cannot appreciate any finite-x correction. Mutual magic also shows a fast convergence with bond dimension, whose specific functional form is however hindered by sampling errors. As a byproduct of our study, we show how Pauli-Markov chains (originally formulated to evaluate magic) resets the state of the art in terms of computing mutual information for MPS. We illustrate this last fact by verifying the logarithmic increase of mutual information between connected partitions at critical points. By comparing mutual information and mutual magic, we observe that, for connected partitions, the latter is typically scaling much slower-if at all-with the partition size, while for disconnected partitions, both are constant in size.

Journal/Review: PHYSICAL REVIEW B

Volume: 110 (4)      Pages from: 45101-1  to: 45101-13

More Information: We thank A. Hamma, T. Haug, G. Lami, and L. Piroli for useful discussions and feedback on the manuscript, and M. C. Banuls, R. Fazio, G. Fux, and X. Turkeshi for collaboration on related topics. P.S.T. acknowledges support from the Simons Foundation through Award No. 284558FY19 to the ICTP. M.D. was partly supported by the MIUR Programme FARE (MEPH) , by the EU-Flagship programme Pasquans2, by the PNRR MUR Project No. PE0000023-NQSTI, and by the PRIN programme (project CoQuS) . M.C. was partially supported by the PRIN 2022 (2022R35ZBF) -PE2-ManyQLowD. M.D. would like to thank the Institut Henri Poincare (UAR 839 CNRS-Sorbonne Universite) for their support. M.D. and E.T. were pa rtly supported by QUANTERA DYNAMITE PCI2022-132919
KeyWords: Quantum entanglement; Boundary effects; Error bars; Fast convergence; Functional forms; Heisenberg chains; Large volumes; Many-body systems; Matrix product state; Mutual informations; Sampling errors; Ground state
DOI: 10.1103/PhysRevB.110.045101

Citations: 2
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