Construction and local equivalence of dual-unitary operators: from
dynamical maps to quantum combinatorial designs
- URL: http://arxiv.org/abs/2205.08842v2
- Date: Mon, 21 Nov 2022 18:06:35 GMT
- Title: Construction and local equivalence of dual-unitary operators: from
dynamical maps to quantum combinatorial designs
- Authors: Suhail Ahmad Rather, S. Aravinda, Arul Lakshminarayan
- Abstract summary: We study the map analytically for the two-qubit case describing the basins of attraction, fixed points, and rates of approach to dual unitaries.
A subset of dual-unitary operators having maximum entangling power are 2-unitary operators or perfect tensors.
A necessary criterion for their local unitary equivalence to distinguish classes is also introduced and used to display various concrete results.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: While quantum circuits built from two-particle dual-unitary (maximally
entangled) operators serve as minimal models of typically nonintegrable
many-body systems, the construction and characterization of dual-unitary
operators themselves are only partially understood. A nonlinear map on the
space of unitary operators was proposed in PRL.~125, 070501 (2020) that results
in operators being arbitrarily close to dual unitaries. Here we study the map
analytically for the two-qubit case describing the basins of attraction, fixed
points, and rates of approach to dual unitaries. A subset of dual-unitary
operators having maximum entangling power are 2-unitary operators or perfect
tensors, and are equivalent to four-party absolutely maximally entangled
states. It is known that they only exist if the local dimension is larger than
$d=2$. We use the nonlinear map, and introduce stochastic variants of it, to
construct explicit examples of new dual and 2-unitary operators. A necessary
criterion for their local unitary equivalence to distinguish classes is also
introduced and used to display various concrete results and a conjecture in
$d=3$. It is known that orthogonal Latin squares provide a ``classical
combinatorial design" for constructing permutations that are 2-unitary. We
extend the underlying design from classical to genuine quantum ones for general
dual-unitary operators and give an example of what might be the smallest sized
genuinely quantum design of a 2-unitary in $d=4$.
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