Area laws and efficient descriptions of quantum many-body states
Ge, Yimin ;  Eisert, Jens

HaupttitelArea laws and efficient descriptions of quantum many-body states
AutorGe, Yimin
AutorEisert, Jens
Seitenzahl10 S.
DDC530 Physik
Auch erschienen inNew Journal of Physics. - 18 (2016), Artikel Nr. 083026
ZusammenfassungIt is commonly believed that area laws for entanglement entropies imply that a quantum many-body state can be faithfully represented by efficient tensor network states—a conjecture frequently stated in the context of numerical simulations and analytical considerations. In this work, we show that this is in general not the case, except in one-dimension. We prove that the set of quantum many-body states that satisfy an area law for all Renyi entropies contains a subspace of exponential dimension. We then show that there are states satisfying area laws for all Renyi entropies but cannot be approximated by states with a classical description of small Kolmogorov complexity, including polynomial projected entangled pair states or states of multi-scale entanglement renormalisation. Not even a quantum computer with post-selection can efficiently prepare all quantum states fulfilling an area law, and we show that not all area law states can be eigenstates of local Hamiltonians. We also prove translationally and rotationally invariant instances of these results, and show a variation with decaying correlations using quantum error-correcting codes.
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Fachbereich/EinrichtungFB Physik
Dokumententyp/-SammlungenWissenschaftlicher Artikel
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This work is licensed under a Creative Commons Attribution 3.0 Unported License.
Erstellt am03.04.2017 - 07:52:10
Letzte Änderung03.04.2017 - 08:07:09
Statische URLhttp://edocs.fu-berlin.de/docs/receive/FUDOCS_document_000000026764