Comments on Hotta’s Quantum Energy Teleportation

[This is a “literature impression“.]

Masahiro Hotta has a series of paper about what he calls “quantum energy teleportation (QET)”, modeled after the well-known notion of quantum teleportation (of information). Although it sounds like crazy crack pot stuff, and they contain the red-flag term “zero-point energy”, the basic physics of Hotta’s work are sound. But they don’t appear to have important consequences for energy transmission.

The idea is to exploit the fact that the ground state of the vacuum in QFT is, in principle, entangled over arbitrary distances. In a toy Alice and Bob model with respective systems A and B, you assume a Hamiltonian for which the ground state is unique and entangled. Then, Alice makes a local measurement on her system A. Neither of the two conditional global states for the joint AB system — conditional on the outcome of the measurement — are eigenstates of the Hamiltonian, and so therefore the average energy must increase for the joint system. The source of this energy is the device Alice used to make the measurement. Now, if Bob were to independently make a measurement of his system, he would find that energy would also necessarily flow from his device into the joint system; this follows from the symmetry of the problem. But if he waits for Alice to transmit to him the outcome of her result, it turns out that he can apply a local unitary to his B system and a subsequent local measurement that leads to a net average energy flow to his equipment. The fact that he must wait for the outcome of Alice’s measurement, which travels no faster than the speed of light, is what gives this the flavor of teleportation.

The first thing to note is that this protocol would work just as good for classically correlated states as for quantum mechanically entangled states. Think of a classically correlated pair of bits. Each has entropy, locally, which can be thought of as lacking the resource of negentropy. But if you measured one (which consumes negentropy) you can extract negentropy from the other (because you then know it’s pure state, and you can get useful work by allowing it to thermalize with any non-zero temperature).

So this isn’t really quantum, except for the important fact that in QFT the vacuum is an entangled state. In other words, correlated states are just lying around “out there”, and don’t need to be generated (using negentropy) like they would in the classical case. This is what might lead one to hope that we can use this naturally available entanglement for energy transmission.

However, the distance this can work over turns out to be very, very tiny. To send E of energy, it only goes over the corresponding relativistic quantum distance scale, i.e. \hbar c/E. Basically, for a particle with de Broglie wavelength determining a certain energy, you can’t send the energy further than the order of a single wavelength! This distance limitation can be fixed by starting with squeezed vacuum, but squeezed vacuums aren’t just available out there; you need to create them, which takes negentropy.

Therefore, this idea does not appear to be useful. It does make me wonder, though, whether you can use the vacuum state for “old fashioned” quantum teleportation of a quantum state. (Presumably you’d use a very low energy mode with wavelength comparable to the distance you want to operate over.) I assume this would never work, but I haven’t thought about it.

Papers:
arXiv:1101.3954
arXiv:1306.5057
PRD:89,012311 / arXiv:1305.3955

Added 2014-2-13: Apparently, Benni Reznik has written on distilling EPR pairs from the vacuum.

arXiv:quant-ph/0310058
arXiv:quant-ph/0212044
arXiv:quant-ph/0008006

[Most of the insight in this post is due to Charlie Bennett.]

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8 Comments

  1. Pingback: Literature impressions | foreXiv

  2. Hi, Riedel! I totally agree with you on the point that QET is not useful for macroscopic energy transmission in daily life, though QET may be expected to play a role in microscopic energy transmisson inside nano-scale devices. It seems that you (and Charlie) do not fully grasp true importance of QET. In general, zero-point energy in many-body systems cannot be extracted by local operations. This fundamental property is called “passivity” of ground states. QET makes “passivity breaking” possible by adopting remote measurements and classical communication. Besides, QET provides a new thought experiment in which energy is extracted out of black holes, reducing horizon area and black hole entropy. (See the reference arXiv:0907.1378 .) QET may become a crucial tool of Quantum Maxwell’s Demons who control both (high-temperature ) classical thermal fluctuation and (low-temperature ) quantum fluctuation. Such an extension of quantum information thermodynamics is interesting and important. Thus QET is more significant for fundamental physics.

  3. P.S. You say “squeezed vacuums aren’t just available out there; you need to create them, which takes negentropy.” However this statement is not correct. Mutual information among zero-point fluctuations in local vacuum regions (energy sender and receiver) remains unchanged after the squeezing. Negentropy is not relevant in this case.

    • > Negentropy is not relevant in this case.

      Can you create the squeezed vacuum with a device that does not require a source of negentropy? Is a toy device described anywhere?

      • The example is found using quantum Hall edge currents. (See the later part of the quoted paper arXiv:1305.3955.) As expanion of early Universe, spatial expansion of edge currents generates the squeezing. This is not accompanied by negentropy generation for zero-point fluctuations in the sender and receiver regions.

        • I’m not talking about generating negentropy in the sender and receiver regions. I’m talking about the consumption of negentropy during the creation of the squeezed state by an artificial process. (Let’s put aside cosmological expansion.) Operating the quantum hall edge current circuit requires negentropy, correct?

          • Not correct. The creation of the squeezed state can be attained, at least in principle, by a unitary prosess for the edge current system. It is reversible, and does not consume negentropy at all. Why do you think the process requires the consumption?

            B.T.W, you quoted our paper arXiv:1306.5057, but the subject is “firewall” and is not related with QET. Have you read it and found some link to QET that we do not know?

  4. Maurel Philippe

    I write in French because i don’t speak english fluently.
    I computed with finite éléments and ddf, by Lagrangian models and Eulerian models.
    Theory of strings is a Lagrangian model and point of view.
    They are Lagrangian strings.
    Why don’t we have a Eulerian point of view ? Wilh Eulerian string ?
    In Quantum phydics, we can’t know at the same time the position and the speed.
    With Lagrangian model, first made for solid, you first access to géométric position than speed by intégration.
    With Eulerian model, first made for fluid, you first access to speed of particle, than position by dérivation.
    Just like in Quantum physics.
    New Eulerian strings Theory ?
    The Eulerian string don’t move and matter gores from string to the next string.

    So instead of thinking to entangled partcles, why not thinking to entangled volume, so as you do ????

    How to entangle volumes ?

    Using two entangled light ray of photon that ” sweep”or illuminate two volumes ? Using a mirror on one of the two light ray in order that They have both the same orientation, E and B.

    So The two volumes should be entangled. So you can have teleportation from one volume to the other one.
    But you have to respect the fact that the same reality can’t be observed at the same time in two différent places. It’s a principle of Quantum physics.

    What do you think of my point of view ?
    Could you make an experiment to prove it works.

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