5 problems

Let $G$ be the Gram matrix associated with the reference states, let $\vec{\psi}$ be a state vector, and let $\tilde{\psi}$ denote the componentwise squared-modulus vector with ent…

Consider catalytic state-transition settings that do not allow external randomness and do not require an asymptotic limit, with catalysts that may become correlated to the system o…

Let a state transition be implemented using unitary operations and a catalyst, where the catalyst remains invariant and arbitrary small errors are allowed on the system but not on…

Let $S_{\mathcal{S}_{+}}(\rho)$ denote the relative entropy of the resource state $\rho$ with respect to the convex hull of the free states, and let ${\Gamma}_{\mathcal{S}}(\rho)$…

Microscopic thermodynamics conjecture. Thermodynamics with microscopic systems should start with a plain ordered commutative monoid $A$, and taking the macroscopic limit should cor…