A Resource Theory of Quantum Energy Teleportation

Abstract

In quantum energy teleportation (QET) a receiver, Bob, extracts energy from a strongly locally passive state after a sender, Alice, measures her part and sends him the outcome. We formulate QET as a resource theory. The free operations are Alice's instruments whose average cannot change Bob's energy (energy-non-signalling instruments), one-way classical communication, and arbitrary channels on Bob's side, with the energy that Bob's device receives booked. The QET potential $W_{\to}$, the most energy Bob can receive by free operations, is a ledger monotone: no free operation increases $W_{\to}$ plus the energy already delivered. When Alice's bond operators commute, the value of $W_{\to}$ over commuting-Kraus instruments has a closed form, which recovers Hotta's optimum for the minimal model. We prove that commuting-Kraus instruments exhaust the free class exactly when the joint eigenvalue vectors of the bond operators are in convex position. In that case $W_{\to}$ is linear in the state, the ledger holds with equality, and two-way classical communication delivers no more energy to Bob than one-way communication. Off convex position the closed form is not a monotone: in a star-coupled model, a free instrument outside the commuting class raises it 6.15-fold. The QET surplus $W_{\to}-W_{\mathrm{loc}}$ is not a monotone in either direction. For a single-qubit receiver we apply the local-ergotropy formula of Salvia, De Palma, and Giovannetti branch by branch; entropic bounds on Bob's yield are valid but loose, and we identify why. Numerical checks cover 12,500 random free operations and transverse-field Ising chains of up to 12 sites.