Long-range quantum energy teleportation and distribution on a hyperbolic quantum network

TL;DR

The paper addresses transferring local quantum energy to distant nodes in large quantum networks. It proposes a hybrid method combining quantum energy teleportation (QET) with quantum state teleportation (QST) on hyperbolic lattices to achieve long-range energy transfer via LOCC. The authors formalize a minimal two-qubit model and extend to hyperbolic {3,q} lattices, showing that energy can be distributed uniformly to many nodes and that receiver energy is negative in expectation while energy is extracted. Simulation on IBM Qiskit confirms homogeneous energy distribution across unit lattices and supports the feasibility of QET/QED in hyperbolic quantum networks. The work suggests practical implications for future large-scale quantum networks and potential energy-delivery-enabled quantum technologies.

Abstract

Teleporting energy to remote locations is new challenge for quantum information science and technology. Developing a method for transferring local energy in laboratory systems to remote locations will enable non-trivial energy flows in quantum networks. From the perspective of quantum information engineering, we propose a method for distributing local energy to a large number of remote nodes using hyperbolic geometry. Hyperbolic networks are suitable for energy allocation in large quantum networks since the number of nodes grows exponentially. To realise long-range quantum energy teleportation, we propose a hybrid method of quantum state telepotation and quantum energy teleportation. By transmitting local quantum information through quantum teleportation and performing conditional operations on that information, quantum energy teleportation can theoretically be realized independent of geographical distance. The method we present will provide new insights into new applications of future large-scale quantum networks and potential applications of quantum physics to information engineering.

Figures (3)

• Figure 1: Complete protocol (A) and quantum circuit (B) for long-range quantum energy teleportation. Alice announces her measurement result to Bob and Charlie. Bob delegates the conditional operation $U_{1}(\mu)$ to Charlie who is spatially very close to Alice and teleports quantum states to Bob. Then Bob can receive $\langle V\rangle$ statistically by measuring his local qubit in $X$ basis. (C) Parameter dependence of theoretical expectation value of teleported energy $\langle E_B\rangle=\mathrm{Tr}[\rho_\text{QET}H_{n_B}]$ to Bob's local system. Bob will receive $-\langle E_B\rangle$ through his measurement device.
• Figure 2: (A) [Upper] Hyperbolic lattice [Lower] unit lattice (B) Protocol of quantum energy distribution; Alice measures $X_0$ and tells her result $\mu\in\{\pm1\}$ to people on the network via classical communication. They can receive energy by applying conditional operation $U_1(\mu)$ and measuring $Z_j$ and $X_j$. (C) Quantum circuits to implement the protocol given in (B).
• Figure 3: (A) [Left] Euclidian lattice of $\{3,6\}$ tiling (yellow) and dual lattice of $\{6,3\}$ tiling (white). [Middle] Hyperbolic lattice of $\{3,7\}$ tiling (yellow) and dual lattice of $\{7,3\}$ tiling (white). [Right] Hyperbolic lattice of $\{3,10\}$ tiling (yellow) and dual lattice of $\{10,3\}$ tiling (white). (B) Expected energy teleported to a node in the unit lattice of each tiling of $\{3,6\},\{3,7\},\{3,10\}$. (C) Simulation of measurement of local operators $X,Z$, evaluated by $10^5$ samplings. Error bars correspond to statistical errors.