Historical research guide · 0308 · 2011
Quantum Energy Teleportation: An Introductory Review
Masahiro Hotta
In one minute
Masahiro Hotta reviews the protocol he proposed in 2008 and named quantum energy teleportation. Start with two distant regions of a system in its ground state — for a field, that means the vacuum. Alice measures the zero-point fluctuation in her region. The measurement costs her energy, because pushing on the vacuum locally always adds energy rather than removing it. Hotta calls that rule the passivity of the vacuum, and it is why nobody extracts zero-point energy at a single spot. But the ground state is entangled, so Alice’s result also tells her something about the fluctuation beside Bob. She sends him the answer down an ordinary classical channel, no faster than light. Bob applies the one operation her answer selects, his region settles below the vacuum’s own energy level, and his device collects the difference as usable energy. The books balance: Alice’s input is never smaller than Bob’s output. Hotta works the protocol through spin chains, harmonic chains and relativistic fields.
Connection
Chapter 6 asks what it actually takes to draw energy out of the ground state, and this is the cleanest published answer: not a local pump, which the vacuum forbids, but a measurement here and a conditioned operation there. It also gives chapter 2 its sharpest teaching example of what a region below the ambient vacuum level really is — a suppressed fluctuation, paid for elsewhere — and chapter 13 an information-theoretic account in which entanglement is the resource being spent.
From the source
Zero-point fluctuation carries real energy: for a harmonic oscillator the ground-state energy comes out as one half of Planck’s reduced constant times the angular frequency, and general interacting many-body systems likewise have subsystems fluctuating with a nonzero energy density in the ground state.Section 2, Capturing the Essence of QET Mechanism, Equation 2
The vacuum is passive: any local unitary operation performed on the vacuum state leaves the field in an excited state, so its average energy increases rather than decreases, and zero-point energy therefore cannot be harnessed by local operations alone — Hotta’s image is a safe underground whose contents really exist but cannot be reached.Section 2, Equation 3
Because the ground state of a many-body system carries entanglement between the fluctuations of its parts, a measurement of the zero-point fluctuation in region A yields a result that contains information about the post-measurement fluctuation in region B — and by passivity that measurement necessarily infuses a positive energy EA into the field at A, which is the protocol’s energy input.Section 2, first step of the protocol, Figures 10 and 11
Told the measurement result over a classical channel, Bob performs the local unitary operation that result selects, which suppresses the one fluctuation component the measurement left standing; the local energy around B then sits below the vacuum’s own level, and by local energy conservation a positive energy EB is released to Bob’s device — the step that gets past the passivity barrier. The total energy afterwards is EA minus EB, so the input is never smaller than the output, and nothing outruns light because only classical information is sent.Section 2, final step of the protocol, Figures 12 and 13
Ground-state entanglement is the physical resource being spent: for the minimal two-qubit model the entanglement consumed by Alice’s measurement is bounded below by a function of the maximum teleported energy, so a large energy output demands a large consumption of ground-state entanglement, and if the ground state is separable there is no correlation to work with at all.Section 6, Summary and Comment, Equation 64
An analogous protocol could be implemented experimentally with quantum Hall edge currents, which behave as a one-dimensional quantum scalar field, and the striking feature of that proposal is an output energy of order 100 microelectronvolts — a magnitude observable with the technology of the day.Section 5, QET with Quantum Field, closing comment
The way in
https://arxiv.org/abs/1101.3954How to cite it
Masahiro Hotta (2011) Quantum Energy Teleportation: An Introductory Review arXiv:1101.3954