Is super-extensive charging power possible with few-body interactions?
In plain words
A quantum battery is a set of N small quantum cells that store energy; charging them together with collective interactions may be faster than charging each cell separately. How that speed-up can grow with N under realistic, few-body interactions is disputed.
Precise statement
For $N$ identical cells with $H_{0}=\sum_i h_i$, a charging Hamiltonian $V(t)$ that is a sum of at most $k$-body terms of bounded norm, and charging power $P=(E(\tau)-E(0))/\tau$, define the advantage $\Gamma=P_{\mathrm{collective}}/P_{\mathrm{parallel}}$. Gyhm, Safranek and Rosa (PRL 2022) proved that $\Gamma$ cannot grow extensively in $N$ without global operations; determine the maximal scaling of $\Gamma$ with N and k under stated constraints (bounded energy per cell, bounded interaction strength, geometric locality), and whether any physical constraint set allows $\Gamma$ to grow with $N$ at fixed $k$.
What would settle it
A proved upper bound on $\Gamma(N, k)$ under stated constraints, matched by an explicit charging protocol.
Status in the literature
Unverified note
A Physical Review Letters article titled 'Super-extensive charging power in the absence of global operations' appeared in September 2026 (doi:10.1103/vjft-c6fp); its assumptions and their relation to the 2022 bound were not checked here.