Historical research guide · 0610 · 2014
Quantum energy teleportation without a limit of distance
Masahiro Hotta · Jiro Matsumoto · Go Yusa
In one minute
Masahiro Hotta, Jiro Matsumoto and Go Yusa work on quantum energy teleportation: Alice measures the zero-point fluctuation in her patch of a quantum field, sends the one-bit result to Bob down an ordinary classical channel, and Bob applies the operation that result selects, releasing usable energy on his side. The protocol works, but earlier versions carried a hard limit — what Bob can collect falls away steeply with the distance between them, capped at one part in twelve pi times that distance, so a long link teleports almost nothing. This letter finds the loophole. The reason for the falloff is that Bob’s region, which momentarily sits below the ambient vacuum level, has to be propped up by positive energy close by, and in the old protocol Alice’s injected energy was the only positive energy available. Put a squeezed vacuum state in the space between them and it supplies that support locally, so the falloff flattens out and the distance stops mattering.
Connection
Chapter 6 asks what it actually takes to draw energy out of the ground state, and Hotta’s introductory review of the protocol — the place to start — is on this site at /library/stm-5aa6b8b006. This sheet is the sequel: it removes the distance limit that kept quantum energy teleportation a millimetre-scale curiosity, and it does so by borrowing a move from cosmology, stretching the space the field lives in, which is why it belongs to chapter 2’s account of what the vacuum is and to chapter 13’s picture of energy, information and geometry as one subject.
From the source
Quantum energy teleportation is energy transport by local operations and classical communication: Alice’s measurement injects a positive energy into the field near her, Bob’s conditioned local operation then releases a positive energy to his device. Only classical information crosses the gap, so nothing outruns light, and because the total energy operator is nonnegative the energy Bob receives is never larger than the energy Alice put in.Introduction; Brief Review of Vacuum-State QET, the paragraph following Equation 8
The vacuum is passive: any local operation intended to extract zero-point energy out of a field actually injects energy and excites the vacuum instead — which is why the zero-point energy can only be glimpsed indirectly, through the Casimir effect, the Unruh effect, and regions where the energy density sits below the vacuum’s own level.Introduction, first paragraph, citing Pusz and Woronowicz 1978
Vacuum-state protocols carry a distance bound. For a 1+1 dimensional massless scalar field the teleported energy over a distance L is at most one divided by twelve pi L in natural units, a consequence of Flanagan’s quantum inequality; the raw falloff of the protocol goes as the inverse sixth power of the distance, improvable to the inverse fourth power by changing Bob’s operator.Equation 1; Distance Bound for Vacuum-State QET, citing Flanagan 1997
The physical reason for the bound is locality plus the nonnegativity of the total energy: a region whose energy density sits below the ambient vacuum level can exist only while a region of sufficient positive energy sits nearby, so in vacuum-state teleportation Bob’s below-vacuum excitation has to stay in the neighbourhood of the positive excitation Alice’s measurement created.Distance Bound for Vacuum-State QET, closing paragraph
The result of the letter: place a squeezed vacuum state between Alice and Bob, with both of them still standing in local vacuum regions of zero energy, and the two-point correlation function is shifted by a length parameter l which may be taken as large as L plus T — so the effective distance for the correlation is far shorter than the physical distance, the positive energy that sustains Bob’s below-vacuum region is supplied by the squeezed region rather than by Alice, and the long-distance damping changes from the inverse sixth power of the distance to no falloff at all.Long-Distance Squeezed-State QET, Equations 16 to 20
The proposed way to build it is an abrupt expansion of the space in which the field lives, described by a scale factor in exactly the way inflationary cosmology describes stretched field modes, which converts vacuum fluctuation into the required squeezed state; in a quantum Hall edge current this means locally extruding the bulk electrons to insert a long detour path between two nearby local vacuum regions, using density control of the kind field-effect transistors already do up to sub-terahertz frequencies — and high-precision squeezing is not required.Long-Distance Squeezed-State QET, Equations 21 and 22 with Figures 2 and 3; Summary
The way in
https://doi.org/10.1103/PhysRevA.89.012311How to cite it
Masahiro Hotta, Jiro Matsumoto, Go Yusa (2014) Quantum energy teleportation without a limit of distance doi:10.1103/PhysRevA.89.012311