Energy as a signature: the sign of the transferred pulse reveals the secret. This metaphor is the key to a new quantum key distribution protocol that uses energy teleportation instead of state measurement. In standard schemes such as BB84 or E91, the secret bit is extracted from measurement outcomes, but here it is hidden in whether Bob gains or loses energy after a local operation.

The protocol begins with Alice and Bob sharing an entangled ground state of a known Hamiltonian. Alice performs a local projective measurement in a randomly chosen basis, injecting energy into her subsystem, and sends the measurement outcome and basis to Bob over a classical channel. Bob applies a local operation depending on the received bit and measures the sign of his local energy change: a negative value corresponds to logical bit 1, a positive value to bit 0. Security rests on the fact that Eve, intercepting the quantum channel, cannot reproduce the energy statistics without computational power of the postBQP class.

Robustness to noise is impressive: with a classical channel error rate up to a threshold of about 25%, the protocol continues to work, and depolarizing noise reduces the energy by a factor (1-p) but does not change its sign. Admixture of the first excited state leads to a sign change of energy with a probability of about 0.2–0.25, which limits the acceptable noise level. Bit errors on Bob's side significantly affect the energy but can be corrected by quantum error correction; phase errors are less critical for small J. For the multiparty extension, the protocol allows detection of a dishonest participant by comparing the signs of measured energies.

Practical implementation requires systems with a sufficiently large energy gap and teleported energy to reliably distinguish the sign. Promising candidates include quantum optical setups, trapped ions, and superconducting circuits, which can provide the necessary parameters. For scaling the multiparty protocol, it is important to use integrable models such as the Thirring model, where ground-state correlators are computed analytically, simplifying calibration and verification. In quantum cryptography, the open problem of protocol robustness against realistic noise and side-channel attacks remains, and this work connects that problem to the precision of preparing ground states of many-body systems, which is computationally hard for classical computers and limits the scaling of multiparty protocols.