13 problems

Let $W_\rho$ be the Wigner function of a quantum state, and let $\mathcal{A}(\alpha,r,L)$ be the smoothness class considered in the paper. Consider testing … against alternatives s…

Let $\rho$ be a quantum statistical model with a full parameter dimension $d^2-1$, and let $\rho'_i$ denote its parameter derivatives. Let $\boldsymbol{\mu}$ be the vector of symme…

Consider the spin-half quantum model in which the state is parametrized by a two-dimensional equatorial-plane parameter, with rotationally symmetric priors and sample size $N$. A n…

Let $\rho^{\otimes n}(\theta)$ be a smooth model of $n$ identical quantum systems, and let $F$ be the scaled information matrix of a measurement on this model. For a mixed-state sp…

Assume that a sequence $\mathcal{S}^{(n)}=\{\rho_{\theta}^{(n)}: \theta\in\Theta\subset\mathbb{R}^{d}\}$ of quantum statistical models is q-LAN at $\theta_0\in\Theta$. Let…

The paper considers the strong-coupling regime in which the coupling parameter satisfies $g\to\infty$. Optimality conjecture. The energy upper bound obtained in the paper should be…

Let an ensemble of rank-$r$ quantum states be given on an infinite-dimensional Hilbert space, and consider its limiting state in the corresponding local asymptotic equivalence prob…

For $\lambda>0$, consider estimating the qubit-state parameter in the Hellinger-distance asymptotic regime, with the corresponding Poisson limit parameter $\mu=n\lambda$. Minimax-c…

Consider quantum Markov chains with mixed independent and identically distributed input states. Local asymptotic normality conjecture. Local asymptotic normality holds for Markov c…

A quantum statistical experiment is a set of density operators on a finite-dimensional Hilbert space. Let two experiments have the same parameter set, and let a trace-preserving po…

Conjugate-observable conjecture. Quantum Fisher information is achieved by measuring a collective observable conjugate to the hamiltonian $H$ in a more general Markov central limit…

Let ${\cal M}$ be the manifold of all invertible $n\times n$ density matrices, let $H$ be a Hamiltonian, and consider the curve of Gibbs states … Equip ${\cal M}$ with the Kubo–Mor…

Scalar-curvature monotonicity conjecture. For any coarse graining $\alpha$, the scalar curvature at a density matrix $\rho$ is smaller than at $\alpha(\rho)$; equivalently, average…