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Questions tagged [representation-theory]

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Is there value in developing a 'physical/relativstic' QIT (discussion)?

My motivation for asking this question is that I've recently been captivated by representation theory and I am incredibly interested in studying the symmetries behind different the operators in QIT. ...
HugeGroupGuy's user avatar
8 votes
3 answers

In Schur-Weyl's duality, why is the commutant of $\pi_k(S_k)$ spanned by $U(d)^{\otimes k}$ matrices?

I'm reading this tutorial paper about quantum state certification. However, I'm confused about the concept of Schur-Weyl duality, explicitly Theorem 35 of the paper. Let $S_k$ denotes the symmetric ...
Sherlock's user avatar
  • 695
4 votes
2 answers

What unitary commutes with all local Pauli operators?

I was thinking about this problem of identifying a set of unitary operations (other than the identity operation) that commute with local pauli $\sigma_X$ and $\sigma_Z$ matrices, i.e. find $U$ such ...
Mohan's user avatar
  • 161
3 votes
0 answers

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) = \...
BlackHat18's user avatar
  • 1,335
2 votes
0 answers

Can we characterize isotropic states via representation theory?

The only bipartite states $\rho$ invariant under any $U\otimes \bar U$ transformation are isotropic states. More precisely, as discussed e.g. in quant-ph/0109124 in Section 4.4, a state $\rho$ is ...
glS's user avatar
  • 25.4k
1 vote
0 answers

Why do phase space representations satisfy a covariance property?

In (Ferrie and Emerson 2008), the authors define (Definition 2 in page 5 of the arxiv) a generic quasi-probability representation of quantum states as any map $\operatorname{Herm}(\mathcal H)\to L^2(\...
glS's user avatar
  • 25.4k