The stabilizer group for an $n$ -qubit state $\ketϕ$ is the set of all invertible local operators (ILO) $g=g_1\otimes g_2\otimes \cdots\otimes g_n,$ $ g_i\in \mathcal{GL}(2,\mathbb{C})$ such that $\ketϕ=g\ketϕ.$ Recently, G. Gour $et$ $al.$ \cite{GKW} presented that almost all $n$ -qubit state $\ketψ$ own a trivial stabilizer group when $n\ge 5.$ In this article, we consider the case when the stabilizer group of an $n$ -qubit symmetric pure state $\ketψ$ is trivial. First we show that the stabilizer group for an n-qubit symmetric pure state $\ketϕ$ is nontrivial when $n\le 4$ . Then we present a class of $n$ -qubit symmetric states $\ketϕ$ with the trivial stabilizer group. At last, we prove that an $n$ -qubit symmetric pure state owns a trivial stabilizer group when its diversity number is bigger than 5, which confirms the main result of \cite{GKW} partly.The stabilizer group for an $n$-qubit state $\ketϕ$ is the set of all invertible local operators (ILO) $g=g_1\otimes g_2\otimes \cdots\otimes g_n,$ $ g_i\in \mathcal{GL}(2,\mathbb{C})$ such that $\ketϕ=g\ketϕ.$ Recently, G. Gour $et$ $al.$ \cite{GKW} presented that almost all $n$-qubit state $\ketψ$ own a trivial stabilizer group when $n\ge 5.$ In this article, we consider the case when the stabilizer group of an $n$-qubit symmetric pure state $\ketψ$ is trivial. First we show that the stabilizer group for an n-qubit symmetric pure state $\ketϕ$ is nontrivial when $n\le 4$. Then we present a class of $n$-qubit symmetric states $\ketϕ$ with the trivial stabilizer group. At last, we prove that an $n$-qubit symmetric pure state owns a trivial stabilizer group when its diversity number is bigger than 5, which confirms the main result of \cite{GKW} partly.

arXiv:1806.01991Jun 6, 20180 citations

Symmetric N-qubit anticoherent states

Dorian Baguette, Thierry Bastin, John Martin

Jun 23, 20140 citations

Multi-qubit stabilizer and cluster entanglement witnesses

M. A. Jafarizadeh, G. Najarbashi, Y. Akbari +1 more

arXiv:0704.2414The European Physical Journal DFeb 29, 200815 citations

The stabilizer for n -qubit symmetric states

Xian Shi

The stabilizer group for an $n$ -qubit state $\ket{\phi}$ is the set of all invertible local operators (ILO) $g=g_1\otimes g_2\otimes \cdots\otimes g_n,$ $ g_i\in \mathcal{GL}(2,\mathbb{C})$ such that $\ket{\phi}=g\ket{\phi}.$ Recently, G. Gour $et$ $al.$ \cite{GKW} presented that almost all $n$ -qubit state $\ket{\psi}$ own a trivial stabilizer group when $n\ge 5.$ In this article, we consider the case when the stabilizer group of an $n$ -qubit symmetric pure state $\ket{\psi}$ is trivial. First we show that the stabilizer group for an n-qubit symmetric pure state $\ket{\phi}$ is nontrivial when $n\le 4$ . Then we present a class of $n$ -qubit symmetric states $\ket{\phi}$ with the trivial stabilizer group. At last, we prove that an $n$ -qubit symmetric pure state owns a trivial stabilizer group when its diversity number is bigger than 5, which confirms the main result of \cite{GKW} partly.The stabilizer group for an $n$-qubit state $\ket{\phi}$ is the set of all invertible local operators (ILO) $g=g_1\otimes g_2\otimes \cdots\otimes g_n,$ $ g_i\in \mathcal{GL}(2,\mathbb{C})$ such that $\ket{\phi}=g\ket{\phi}.$ Recently, G. Gour $et$ $al.$ \cite{GKW} presented that almost all $n$-qubit state $\ket{\psi}$ own a trivial stabilizer group when $n\ge 5.$ In this article, we consider the case when the stabilizer group of an $n$-qubit symmetric pure state $\ket{\psi}$ is trivial. First we show that the stabilizer group for an n-qubit symmetric pure state $\ket{\phi}$ is nontrivial when $n\le 4$. Then we present a class of $n$-qubit symmetric states $\ket{\phi}$ with the trivial stabilizer group. At last, we prove that an $n$-qubit symmetric pure state owns a trivial stabilizer group when its diversity number is bigger than 5, which confirms the main result of \cite{GKW} partly.

Chinese Physics BOct 1, 20183 citations

Local unitary group stabilizers and entanglement for multiqubit symmetric states

Curt D. Cenci, David W. Lyons, Scott N. Walck

We refine recent local unitary entanglement classification for symmetric pure states of $n$ qubits (that is, states invariant under permutations of qubits) using local unitary stabilizer subgroups and Majorana configurations. Stabilizer subgroups carry more entanglement distinguishing power than do the stabilizer subalgebras used in our previous work. We extend to mixed states recent results about local operations on pure symmetric states by showing that if two symmetric density operators are equivalent by a local unitary operation, then they are equivalent via a local unitary operation that is the {\em same} in each qubit. A geometric consequence, used in our entanglement classification, is that two symmetric pure states are local unitary equivalent if and only if their Majorana configurations can be interchanged by a rotation of the Bloch sphere.We refine recent local unitary entanglement classification for symmetric pure states of $n$ qubits (that is, states invariant under permutations of qubits) using local unitary stabilizer subgroups and Majorana configurations. Stabilizer subgroups carry more entanglement distinguishing power than do the stabilizer subalgebras used in our previous work. We extend to mixed states recent results about local operations on pure symmetric states by showing that if two symmetric density operators are equivalent by a local unitary operation, then they are equivalent via a local unitary operation that is the {\em same} in each qubit. A geometric consequence, used in our entanglement classification, is that two symmetric pure states are local unitary equivalent if and only if their Majorana configurations can be interchanged by a rotation of the Bloch sphere.

arXiv:1011.5229Nov 23, 20104 citations

The stabilizer group for an

n

-qubit state

\ketϕ

is the set of all invertible local operators (ILO)

g=g_1\otimes g_2\otimes \cdots\otimes g_n,

$ g_i\in \mathcal{GL}(2,\mathbb{C})$ such that

\ketϕ=g\ketϕ.

Recently, G. Gour

et

al.

\cite{GKW} presented that almost all

n

-qubit state

\ketψ

own a trivial stabilizer group when

n\ge 5.

In this article, we consider the case when the stabilizer group of an

n

-qubit symmetric pure state

\ketψ

is trivial. First we show that the stabilizer group for an n-qubit symmetric pure state

\ketϕ

is nontrivial when

n\le 4

. Then we present a class of

n

-qubit symmetric states

\ketϕ

with the trivial stabilizer group. At last, we prove that an

n

-qubit symmetric pure state owns a trivial stabilizer group when its diversity number is bigger than 5, which confirms the main result of \cite{GKW} partly.

The stabilizer group for an

n

-qubit state

\ket{\phi}

is the set of all invertible local operators (ILO)

g=g_1\otimes g_2\otimes \cdots\otimes g_n,

$ g_i\in \mathcal{GL}(2,\mathbb{C})$ such that

\ket{\phi}=g\ket{\phi}.

Recently, G. Gour

et

al.

\cite{GKW} presented that almost all

n

-qubit state

\ket{\psi}

own a trivial stabilizer group when

n\ge 5.

In this article, we consider the case when the stabilizer group of an

n

-qubit symmetric pure state

\ket{\psi}

is trivial. First we show that the stabilizer group for an n-qubit symmetric pure state

\ket{\phi}

is nontrivial when

n\le 4

. Then we present a class of

n

-qubit symmetric states

\ket{\phi}

with the trivial stabilizer group. At last, we prove that an

n

-qubit symmetric pure state owns a trivial stabilizer group when its diversity number is bigger than 5, which confirms the main result of \cite{GKW} partly.

We refine recent local unitary entanglement classification for symmetric pure states of

n

qubits (that is, states invariant under permutations of qubits) using local unitary stabilizer subgroups and Majorana configurations. Stabilizer subgroups carry more entanglement distinguishing power than do the stabilizer subalgebras used in our previous work. We extend to mixed states recent results about local operations on pure symmetric states by showing that if two symmetric density operators are equivalent by a local unitary operation, then they are equivalent via a local unitary operation that is the {\em same} in each qubit. A geometric consequence, used in our entanglement classification, is that two symmetric pure states are local unitary equivalent if and only if their Majorana configurations can be interchanged by a rotation of the Bloch sphere.