9 problems

Consider AMP reconstruction applied to quantum state tomography experiments for Hadamard and GHZ states, with state preparation fidelity denoted by…

Let $d=2^n$ be the Hilbert-space dimension for an $n$-qubit system, and consider quantum state tomography in the high-dimensional regime where the ratio of the number of measuremen…

Let $\boldsymbol{\rho}^\star$ be the MPO state considered in the recovery results, and let the results in the Frobenius-norm recovery guarantee and the recovery-error bounds for va…

Let a cyclic $t$-design in dimension $d$ be a finite orbit of a unitary acting on quantum states whose decohered probability vectors form a simplex $t$-design. Cyclic 2-design exis…

Let $\Delta_d$ denote the $d$-point probability simplex, and let a simplex $t$-design be a collection of points in $\Delta_d$ whose moments agree with those of the uniform simplex…

Let $Q$ be the number of Haar-random rank-one POVMs and $M$ the number of measurements performed for each POVM. The statistical recovery bound in the paper requires a total number…

Let $\mathcal{A}^{Q}:\mathbb{C}^{d^n\times d^n}\rightarrow\mathbb{R}^{KQ}$ be the linear map induced by $Q$ random unitary matrices, and let $\overline{\mathbb{X}}_{\overline{r}}$…

Adaptivity necessity conjecture. Achieving the optimal rate for incoherent measurements requires logarithmically many rounds of adaptivity.

An exact $t$-design is a collection of vectors reproducing the relevant $t$-th moments of the uniform distribution, and Kuperberg's construction uses only…