publication . Other literature type . Article . Preprint . 2017

The tensor rank of tensor product of two three-qubit W states is eight

Chen, Lin; Friedland, Shmuel;
  • Published: 28 Aug 2017
  • Publisher: Elsevier BV
Abstract
We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.
Subjects
arXiv: Computer Science::Emerging Technologies
free text keywords: Geometry and Topology, Algebra and Number Theory, Numerical Analysis, Discrete Mathematics and Combinatorics, Qubit, Mathematics, Tensor product, W state, Pure mathematics, Combinatorics, Tensor rank, Kronecker product, symbols.namesake, symbols, Upper and lower bounds, Quantum Physics, Mathematics - Combinatorics
Related Organizations
21 references, page 1 of 2

3. For B ∈ {e1 ⊗ e1 ⊗ e2, e1 ⊗ e2 ⊗ e1} the rank of W + tB is three for all t 6= −1. The rank of W − B is two.

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