Mixed states in one spatial dimension: decompositions and correspondence with nonnegative matrices

@article{Cuevas2019MixedSI,
  title={Mixed states in one spatial dimension: decompositions and correspondence with nonnegative matrices},
  author={G. D. L. Cuevas and T. Netzer},
  journal={arXiv: Quantum Physics},
  year={2019}
}
  • G. D. L. Cuevas, T. Netzer
  • Published 2019
  • Physics, Mathematics
  • arXiv: Quantum Physics
  • We study six natural decompositions of mixed states in one spatial dimension: the Matrix Product Density Operator (MPDO) form, the local purification form, the separable decomposition (for separable states), and their three translational invariant (t.i.) analogues. For bipartite states diagonal in the computational basis, we show that these decompositions correspond to well-studied factorisations of an associated nonnegative matrix. Specifically, the first three decompositions correspond to the… CONTINUE READING

    Figures and Tables from this paper.

    Tensor decompositions on simplicial complexes with invariance.
    • 3
    • Open Access
    Approximate tensor decompositions: disappearance of many separations
    Tensor decompositions: invariance and computational complexity

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 40 REFERENCES
    Separability for mixed states with operator Schmidt rank two
    • 3
    • Open Access
    PEPS as ground states: Degeneracy and topology
    • 151
    • Open Access
    Matrix-product operators and states: NP-hardness and undecidability.
    • 37
    • Open Access
    Matrix product state representations
    • 575
    • Open Access
    Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank
    • 16
    • Open Access