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Laser Physics

Constructing five qutrit absolutely maximally entangled state via recurrence relation

Xin-Wei Zha, Irfan Ahmed, Yanpeng Zhang

Published Jun 1, 2020• 7 citations
Publisher

Abstract

Abstract Recently, Che et al presented a recurrence relation of multi-qubit states. Regarding this inspiration, we give and extend the recurrence relation of multi-qubit states to the recurrence relation of maximally qutrit entangled states. We also establish absolutely maximally entangled five qutrits states via maximally entangled four qutrits states. We also demonstrate that such a state is the 2-uniform state of five qutrits states.

DOI
10.1088/1555-6611/ab8d2f

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A pure quantum state of NNN subsystems with ddd levels each is called kkk-multipartite maximally entangled state, which we call a kkk-uniform state, if all its reductions to kkk qubits are maximally mixed. Recently, Goyeneche and Zyczkowski proposed a method of constructing kkk-uniform states via orthogonal arrays, by which, we will also propose a new method to construct quantum states with orthogonal arrays in this paper, which is the method of increasing phase parameters. We can find the quantum states constructed via our new method by using the same orthogonal array, for four-qubit quantum states, not only are they 1-uniform states, also may become maximally entangled states; for five-qubit quantum states, we find that it can make the original 1-uniform states into 2-uniform states. In particular, for four-qubit quantum states, we can construct a series of new forms of maximally entangled states via our new method.