Quantum Key Distribution by Quantum Energy Teleportation

TL;DR

The paper proposes and analyzes a quantum key distribution protocol based on quantum energy teleportation (QET), where a shared ground-state Hamiltonian enables key readout via the sign of the energy change at the recipient’s site after a one-bit feed-forward. It provides a two-party protocol, extends to multiparty authentication, and compares the approach to standard QKD schemes such as E91 and BB84, highlighting unique readout and verification features like the energy-gap fidelity witness. Security is treated in a composable framework, with a detailed MITM analysis showing resilience unless the adversary reaches postBQP capabilities, and a natural analogue of QBER appears as the sign error rate $Q_{ ext{sign}}$. The work also investigates robustness to classical communication errors and several noise models in the quantum resource state, presenting thresholds and strategies (including random measurement bases and integrable Hamiltonians) to enable scalable, verifiable QET-based QKD. While experimental realization is challenging due to small teleported energies, the protocol offers a novel route to secure quantum communication with intrinsic state verification and potential multiparty cryptographic primitives.

Abstract

Quantum energy teleportation (QET) is a process that leverages quantum entanglement and local operations to transfer energy between two spatially separated locations without physically transporting particles or energy carriers. We construct a QET-based quantum key distribution (QKD) protocol and analyze its security and robustness to noise in both the classical and the quantum channels. We generalize the construction to an $N$-party information sharing protocol, possessing a feature that dishonest participants can be detected.

Figures (9)

• Figure 1: Bob's teleported energy expectation value $\Tr[(\rho_{B}-\rho_{g_s})H_B]$ (\ref{['eq:QET']}) in arbitrary units, when Alice's measurement basis $\sigma_A$ is $X$, $Y$ or random, i.e. $X$ or $Y$ with equal probability. The horizontal axis is the coupling $J$ (\ref{['H012']}). We see that there is an optimal value of $J$ for the protocol, where Bob's energy is at the minimum.
• Figure 2: Bob's measured energy expectation value in arbitrary units when the bit $b\oplus1$ is used by Bob for rotation, instead of Alice's measured bit $b$. Alice's measurement basis $\sigma_A$ is $X$, $Y$ or random, i.e. $X$ or $Y$ with equal probability. The horizontal axis is the coupling $J$ (\ref{['H012']}). We see that the energy is positive in contrast Fig. \ref{['fig:QET_random_base']}, as expected. There is an optimal value of $J$ for the protocol, where Bob's energy is at the maximum.
• Figure 3: Bob's teleported energy in the presence of a classical communication error with probability $p$. Left: Hamiltonian \ref{['eq:Hamiltonian']} with $J=1$. Right: Hamiltonian \ref{['eq:Hamiltonian']} with $N=2$. The vertical threshold line is located at $p=0.25$.
• Figure 4: Energy gap between the ground state energy and first excited state energy of the Hamiltonian \ref{['H012']}.
• Figure 5: Bob's teleported energy in the presence of a probabilistic mixture of the ground state with the first excited state with probability $p$ (\ref{['Mix']}).