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Questions tagged [t-designs]

For questions about quantum t-designs: probability distributions over states or unitaries that replicate specific properties of the Haar distribution.

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How to compute Haar average over the unitary group of a ratio of homogeneous polynomials?

I am interested in the following Haar average over the unitary group: $\mathbb{E}_U\Big[\frac{tr(U^{\otimes p}|j\rangle\langle j|(U^\dagger)^{\otimes p}\rho \otimes \sigma ...)}{tr(U^{\otimes q}|j\...
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Optimality of the SWAP test versus weak Schur sampling for testing unitarily invariant properties

Consider the following setting. I am either given the density matrix $|\psi\rangle \langle \psi|^{\otimes k}$ or the density matrix $\frac{\mathbb{I}^{\otimes k}}{2^{nk}}$, where $\mathbb{I}$ is the $...
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