6 problems

Critical-point conjecture. The phase transition occurs at the critical point

Let $\rho^{AEB}$ be a tripartite quantum state, let $\rho^{AE}$ and $\rho^{EB}$ denote its reduced states, and define the Petz recovery map $R:E\to EB$ by … Writing…

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

Let $X\in\mathcal{A}\otimes\mathcal{B}$ be a selfadjoint operator with $\langle X\rangle_{ss}^{out}=0$. Let $\mathbb{F}_n(X)$ denote the associated fluctuations operator, and let…

Conditional-mutual-information stability conjecture. Small conditional mutual information implies that $\rho_{ABC}$ is a small perturbation of a quantum Markov chain.

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…