Questions tagged [symmetry]

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A question on a subset of projectors onto symmetric subspace

Use $\text{perm}_t$ to denote the set of all permutations among $t$ items. For any particular subset $S\subseteq\{0,1\}^n$ and any $\sigma\in \text{perm}_t$, we define \begin{align} P_S(\sigma) = \sum_{x_1,\ldots,x_t\in…
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Why does Schur's lemma imply that $\int \sigma^{\otimes n}_{HK} d(\sigma)$ must be a multiple of the identity on the symmetric subspace?

I am trying to understand Lemma 2 in this paper. Consider a state $\tau_{H^n}=\int \sigma^{\otimes n}_{H} \mu(\sigma)$ where $\mu(\sigma)$ is the measure on the space of density operators on a single subsystem induced by the Hilbert-Schmidt…
user1936752
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Symmetries of maximally bi-partite pure entangled states

My question focuses on bi-partite pure systems, but I am also interested in answers focusing on 2-qubit systems (this is actually the case I'm mostly interested in). While being written in a different manner, many entangled state are actually…
Marco Fellous-Asiani
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What is $\mathbb{Z}_2$ symmetry?

I encountered the notion of $\mathbb{Z}_2$ symmetry in an article. Can someone give a definition?
cnada
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Symmetry with uniform state in Quantum Walk

In the sequel, I follow the De Wolf's lecture notes and its chapter about Quantum Walk. I assume $G=(V,E)$ to be an undirected graph with $n$ the number of vertices. Usual restrictions for $G$ are that it must be connected and not bi-partite. The…
deb2014
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