The coupled cluster method and entanglement in three fermion systems

Péter Lévay, Szilvia Nagy, János Pipek, Gábor Sárosi

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Abstract

The Coupled Cluster (CC) and full CI expansions are studied for three fermions with six and seven modes. Surprisingly the CC expansion is tailor made to characterize the usual stochastic local operations and classical communication (SLOCC) entanglement classes. It means that the notion of a SLOCC transformation shows up quite naturally as a one relating the CC and CI expansions, and going from the CI expansion to the CC one is equivalent to obtaining a form for the state where the structure of the entanglement classes is transparent. In this picture, entanglement is characterized by the parameters of the cluster operators describing transitions from occupied states to singles, doubles, and triples of non-occupied ones. Using the CC parametrization of states in the seven-mode case, we give a simple formula for the unique SLOCC invariant I. Then we consider a perturbation problem featuring a state from the unique SLOCC class characterized by I. For this state with entanglement generated by doubles, we investigate the phenomenon of changing the entanglement type due to the perturbing effect of triples. We show that there are states with real amplitudes such that their entanglement encoded into configurations of clusters of doubles is protected from errors generated by triples. Finally we put forward a proposal to use the parameters of the cluster operator describing transitions to doubles for entanglement characterization. Compared to the usual SLOCC classes, this provides a coarse grained approach to fermionic entanglement.

Original languageEnglish
Article number012203
JournalJournal of Mathematical Physics
Volume58
Issue number1
DOIs
Publication statusPublished - Jan 1 2017

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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