Quantum energy teleportation
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.
[1] The protocol was first experimentally demonstrated in 2023 by Kazuki Ikeda who used superconducting quantum computers to show the energy teleportation effect.
[3] 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.
[4] 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.
These regions possess a negative energy density since the vacuum fluctuations already represent the zero-energy state.
[5] Conceptually, the QET protocol can be described by three steps: Intuitively, one would not expect to be able to extract energy from the ground state in such a manner.
The derivation in this section follows the work done by Masahiro Hotta in "Quantum Energy Teleportation in Spin Chain Systems".
[5] This is an important result of the measurement process as the point of the QET protocol is for Alice to inject a positive quantity of energy into the spin chain.
can be shifted by adding constants such that the expectation value of the local energy operators are each zero,
Since the expectation value of the local energy operators are zero, it implies that the lowest eigenvalue of
So, for Alice to extract the energy she first deposited to the system during the measurement process she must first restore the ground state.
To recreate the entanglement, Alice would need to use non-local operators which inherently require energy.
[2] The basic QET protocol discussed early was verified using several IBM superconducting quantum computers.
These quantum computers provide two connected qubits with high precision for controlled gate operation.
The classical communication of measurement results was on the order of 10 nanoseconds and was much faster than the energy propagation timescale of the system.
Bob then applied a conditional rotational operation on his qubit dependent on Alice's measurement.
Bob then performed a local measurement on his state to extract energy from the system
For quantum computers, energy scales tend to be limited by the qubit transition frequency which is often on the order of GHz.
Ikeda experimented with varying the parameters in the Hamiltonian, specifically the local energy
Depending on the experimental parameters, Bob would receive around 1-5% of Alice's inputted energy.
Quantum error correction is important specifically for implementing QET protocols experimentally due to the high precision needed to calculate the negative energy Bob receives in the QET protocol.
Error correction in this experiment greatly improved the amount of energy Bob could extract from the system.
In some cases without error correction, Bob's extracted energy would be positive, indicating the QET protocol did not work.
The quantum error correction employed in this experiment allowed Ikeda to observe negative expectation values of the extracted energy
High precision is also required for experimental implementation of QET due to the subtle effects of negative energy density.
Since negative energy densities are a consequence of vacuum fluctuations, they can easily be overshadowed by measurement noise in the instrumentation.
So, higher precision can lead to better distinguishability between negative energy signals and noise.
