Quantum energy teleportation

Quantum energy teleportation (QET) is an application of quantum information science. It is a variation of the quantum teleportation protocol. Quantum energy teleportation allows energy to be teleported from a sender to a receiver, regardless of location. This protocol works by having the sender inject energy into the quantum vacuum state which the receiver can then extract positive energy from. QET differs from quantum teleportation as instead of information about an unknown state being teleported from a sender to a receiver, energy is transferred instead. This procedure does not allow faster-than-light transfer of energy and does not allow the spontaneous creation of energy. The sender and receiver share a pair of entangled spins in a spin chain. Energy can be teleported from the sender, Alice, to the receiver, Bob, instantly by using the effects of local operators. However, in order for Bob to extract this energy from his spin he requires a classically communicated signal from Alice. Since this classical signal cannot be transmitted faster than the speed of light, the speed at which energy can be transferred from Alice to Bob is also limited by the speed of light. Quantum energy teleportation was first proposed conceptually by Masahiro Hotta in 2008. The protocol was first experimentally demonstrated in 2023 by Kazuki Ikeda who used superconducting quantum computers to show the energy teleportation effect.

QET mechanisms There are two main factors involved in how QET works: how energy is transferred from Alice to Bob, and how Bob can extract energy from his spin.

Spin chains

QET is studied through analyzing spin chain models. A spin chain is a type of model where a one dimensional chain of sites are assigned certain spin value at each site, typically +1/2 or -1/2 when considering spin-1/2. The spin of one individual site can interact with the spin of its adjacent neighbours, causing the entire system to be coupled together. Spin chains are useful for QET due to the fact that they can be entangled even in the ground state. This means that even without external energy being added to the system, the ground state exhibits quantum correlations across the chain. Alice and Bob are both in possession of an entangled state from a spin chain system. This can provide a rudimentary explanation of how energy can be transferred from Alice's spin to Bob's spin, since any action on Alice's spin can have an effect on Bob's spin.

Vacuum fluctuations The other key component to understanding the QET mechanism is vacuum fluctuations and the presence of negative energy density regions within the energy distribution of a quantum mechanical system. Vacuum fluctuations are a consequence of the Heisenberg uncertainty principle, specifically the uncertainty between the field amplitude and its conjugate momentum, which is analogous to the position-momentum uncertainty principle.

The commutation relation, [ φ ( x , y , z ) , Π ( x ′ , y ′ , z ′ ) ] = i ℏ δ ( x − x ′ ) δ ( y − y ′ ) δ ( z − z ′ ) {\textstyle [\varphi (x,y,z),\Pi (x',y',z')]=i\hbar \delta (x-x')\delta (y-y')\delta (z-z')} , gives rise to uncertainty in energy densities at different spatial points. Consequently, the energy fluctuates around the zero-point energy density of the state The vacuum fluctuations in certain regions can have lower amplitude fluctuations due to the effect of local operations. These regions possess a negative energy density since the vacuum fluctuations already represent the zero-energy state. Therefore, fluctuations of lower amplitude relative to the vacuum fluctuations represent a negative energy density region. Since the entire vacuum state still has zero-energy, there exist other regions with higher vacuum fluctuations with a positive energy density. Negative energy density in the vacuum fluctuations plays an important role in QET since it allows for the extraction of energy from the vacuum state. Positive energy can be extracted from regions of positive energy density which can be created by regions of negative density region elsewhere in the vacuum state.

QET in a spin chain system

Framework of the quantum energy teleportation protocol The QET process is considered over short time scales, such that the Hamiltonian of the spin chain system is approximately invariant with time. It is also assumed that local operations and classical communications (LOCC) for the spins can be repeated several times within a short time span. Alice and Bob share entangled spin states in the ground state | g ⟩ {\textstyle |g\rangle } with correlation length ℓ {\textstyle \ell } . Alice is located at site n A {\textstyle n_{A}} of the spin chain system and Bob is located at site n B {\textstyle n_{B}} of the spin chain system such that Alice and Bob are far away from each other, | n A − n B | ≫ 1 {\textstyle |n_{A}-n_{B}|\gg 1} .

The QET protocol Conceptually, the QET protocol can be described by three steps:

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