Entangling power of symmetric two-qubit quantum gates
- URL: http://arxiv.org/abs/2107.12653v1
- Date: Tue, 27 Jul 2021 08:06:32 GMT
- Title: Entangling power of symmetric two-qubit quantum gates
- Authors: D. Morachis and Jes\'us A. Maytorena
- Abstract summary: capacity of a quantum gate to produce entangled states on a bipartite system is quantified in terms of the entangling power.
We focus on symmetric two-qubit quantum gates, acting on the symmetric two-qubit space.
A geometric description of the local equivalence classes of gates is given in terms of the $mathfraksu(3)$ Lie algebra root vectors.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The capacity of a quantum gate to produce entangled states on a bipartite
system is quantified in terms of the entangling power. This quantity is defined
as the average of the linear entropy of entanglement of the states produced
after applying a quantum gate over the whole set of separable states. Here we
focus on symmetric two-qubit quantum gates, acting on the symmetric two-qubit
space, and calculate the entangling power in terms of the appropriate
local-invariant. A geometric description of the local equivalence classes of
gates is given in terms of the $\mathfrak{su}(3)$ Lie algebra root vectors.
These vectors define a primitive cell with hexagonal symmetry on a plane, and
through the Weyl group the minimum area on the plane containing the whole set
of locally equivalent quantum gates is identified. We give conditions to
determine when a given quantum gate produces maximally entangled states from
separable ones (perfect entanglers). We found that these gates correspond to
one fourth of the whole set of locally-distinct quantum gates. The theory
developed here is applicable to three-level systems in general, where the
non-locality of a quantum gate is related to its capacity to perform non-rigid
transformations on the Majorana constellation of a state. The results are
illustrated by an anisotropic Heisenberg model, the Lipkin-Meshkov-Glick model,
and two coupled quantized oscillators with cross-Kerr interaction.
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