Wednesday, May 13, 2015

Information transfer without energy exchange

While I was writing up my recent paper on classical information exchange, a very interesting new paper appeared on quantum information exchange
    Information transmission without energy exchange
    Robert H. Jonsson, Eduardo Martin-Martinez, Achim Kempf
    Phys. Rev. Lett. 114, 110505 (2015)
    arXiv:1405.3988 [quant-ph]
I was visiting Achim’s group two weeks ago and we talked about this for a bit.

In their paper the authors study the communication channels in lower dimensional spaces by use of thought experiments. If you do thought experiments, you need thought detectors. Named “Unruh De-Witt detectors” after their inventors such detectors are the simplest systems you can think of that detect something. It’s a state with two energy levels and it couples linearly to the field you want to detect. A positive measurement results in an excitation of the detector’s state, and that’s pretty much it. No loose cables, no helium leaks, no microwave ovens.

Equipped with such a thought detector, you can then introduce Bob and Alice and teach them to exchange information by means of a quantum field, in the simplest case a massless scalar field. What they can do depends on the way the field is correlated with itself at distant points. In a flat space-time with three spatial dimensions, the field only correlates with itself on the lightcone. But in lower dimensions this isn’t so.

The authors then demonstrate just exactly how Alice can use the correlations to send information to Bob in two spatial dimensions, or 2+1 dimensional space-time as the physicists like to say. They further show that Alice can submit a signal without it drowning in quantum noise. Alice submits information not by sending a quantum of the field, but by coupling and decoupling her detector to the field’s vacuum state. The correlations in the field then imply that whether her detector is coupled or not affects how the field excites Bob’s detector.

Now this information exchange between Bob and Alice is always slower than the speed of light so you might wonder why that is interesting. It is interesting because Alice doesn’t send any energy! While the switching of the detectors requires some work, this is a local energy requirement which doesn’t travel with the information.

Okay you might say then, fine, but we don’t live in 2+1 dimensional space-time. That’s right, but we don’t live in three plus one dimensional flat space-time either: We live in a curved space-time. This isn’t further discussed in the paper but the correlations allowing for this information exchange without energy can also exist in some curved backgrounds. The interesting question is then of course, in which backgrounds and what does this mean for our sending of information into black holes? Do we really need to use quanta of energy for this or is there a way to avoid this? And if it can be avoided, what does it mean for the information being stored in black holes?

I am sure we will hear more about this in the future...


  1. We should call it "ghost information"

  2. I think this part of the post needs fixing, I'm not really sure what you tried to say:

    "...then imply that her whether her detector is coupled ..."

  3. Reversibly connect a capacitive or inductive load to a transmission line. They change the line's observed properties. In the Aharonov–Bohm and Aharonov–Casher effects, measurement occurs within regions wherein E,B = 0 (electric and magnetic fields are zero). Would this apply?

    A theoretician's detector lacks an amortized depreciation tax write-down (financial dissipation, economics invariably being lossy).

  4. Very interesting but unbelievable! The entire field from one end to the other end has some energy. When Alice disturbs the field that energy must change because Alice puts in energy at her end. Similarly Bob also spends energy. So it must travel. This is not like usual entanglement where particles are already entangled before travelling. What is the catch? Isn’t energy conserved in 2+1 dimensions? Also I understand there is some result of information theory that every bit is equivalent to energy of kT ln(2). Is that right?

  5. tobychev,

    Thanks, I fixed that sentence.

  6. kashyap,

    Yes, but the energy isn't transmitted. Sure, energy is conserved. The thing is that the quantum vacuum already contains correlations. It's just that one can't normally use these to submit information. Yes, there is such a result in information theory, which is why this is interesting. It is about changing a bit of information though, and it is for a thermal system. Best,


  7. Why can't this system be seen as transmitting information without transmitting energy:

    Old Sciam article. Look at the first diagram on page 99. Blocking IDLER1 seems to cause information to be transmitted between the signal detector and the idler beam despite the fact that no energy flows between the two points.

    But I'm a little confused about what is happening at down converter 2.

  8. Here's a paper about the fact that Landauer's principle works for any conserved quantity, not just energy.

    In thermodynamics one considers thermal systems and the maximization of entropy subject to the conservation of energy. A consequence is Landauer's erasure principle, which states that the erasure of 1 bit of information requires a minimum energy cost equal to kTln(2) where T is the temperature of a thermal reservoir used in the process and k is Boltzmann's constant. Jaynes, however, argued that the maximum entropy principle could be applied to any number of conserved quantities which would suggest that information erasure may have alternative costs. Indeed we showed recently that by using a reservoir comprising energy degenerate spins and subject to conservation of angular momentum, the cost of information erasure is in terms of angular momentum rather than energy. Here we extend this analysis and derive the minimum cost of information erasure for systems where different conservation laws operate. We find that, for each conserved quantity, the minimum resource needed to erase 1 bit of memory is λ−1ln(2) where λ is related to the average value of the conserved quantity. The costs of erasure depend, fundamentally, on both the nature of the physical memory element and the reservoir with which it is coupled.

  9. Alice and Bob. Nice intersection with cryptographic protocol analysis/descriptions, where Alice and Bob are the first and second parties in protocols, Eve is the Eavesdropper, Mallory is the malicious attacker, Victor is the verifier, etc.

  10. One can *never* use entanglement to directly send information between the two entangled objects. Entanglement is just the most general quantum description of all the correlations that have evolved due to the mutual interactions of the subsystems in the past.

    The entanglement found between fields in two regions in quantum field theory is absolutely no different in this respect.

    If one uses a massless field to send the information, the transmission may be described in terms of virtual particles which are a different concept than real particles. But they are not "mutually exclusive in the physical sense". If a calculation uses virtual particles, it doesn't mean that the occupation numbers of the information-carrying field were zero at all times. Indeed, if they were zero at all times, they couldn't have carried any information.

  11. ppnl,

    Yes, good point. You can of course send information without it being accompanied by energy, and you don't even need quantum mechanics for this. We can just agree that if you don't show up by 8pm, we will meet later at the movies, so then your non-appearance has sent me information without any energy. But we previously had to agree on some code for this. The quantum information people have all kinds of protocols for what exactly they mean with information transfer, but unfortunately I'm not very familiar with them. Whenever you get a message by the absence of a signal though, you first must have agreed on what is being done. Best,


  12. kashyap,

    Sorry, I realize my explanation didn't make much sense. It should have been 'information outside the lightcone'. What I actually meant, if you look at the paper, is that in 1+1 dimensions the Greensfunction has support not only on the lightcone. Best,


  13. Bee,
    Thanks. But I still suspect there is some catch about energy conservation.Also their ideas of entanglement are completely different from all the previous ideas. But, of course, I do not know enough to write
    a challenging paper! My guess is that this paper will be soon challenged!

  14. kashyap,

    I don't know what you mean, really. It's standard quantum field theory, equal time commutation relations. The thing is just that in general, time-dependent curved backgrounds these relations can get quite difficult. And I don't really know why you think energy isn't conserved. You do have to invest energy to produce the signal, so to speak, it's just that the energy doesn't generally travel with the information, in some sense. Best,


  15. Saying "If I don't show up by 8pm, we will meet later" sends information without energy is surely like saying bit 0 requires no energy, but bit 1 does. Yeah, OK, but in the general case you cannot send information by that method - you needs zeroes and ones to send information, so surely you need energy.

  16. Entanglements is about instantons, I think, look at the teleportation experiments in Wien, as instance, and to say this is outside the lightcone, and SLOWER than speed of light is nonsense then... Does it even have a lifetime then (no time uncertainty)?

    The message is recieved instantly, but if there is no change how can there be a message, and how can you know of it if there is one? Absence of waited message is no good explanation, according to me.

    Entanglement is also maybe flexible, tolerate some disturbance without change, but we don't know how big stress it tolerates, probably not much, and then the coherence is gone.

    Interesting take on things.

  17. Sabine, I am afraid that you're confused. In all - curved, n-dimensional - spacetimes, the equal-time commutators are still as simple as the usual ones. The field only has a nonzero commutator with its time (coordinate perpendicular to the slice) derivative and the commutator is the delta-function times the obvious thing dictated by the local Lorentz symmetry.

    Equal time commutators are simple because they follow from the canonical quantization. It's only the non-equal time commutators that become tough - they're nonzero inside the timelike plus lightlike region, and encode some propagators. And those (for massless fields) are different in even and odd dimensions. The Hyugens principle behaves differently. But none of these complicated functions ever affect equal-time commutators. At equal times, almost all the separations are spacelike, so the commutators are zero except for one point.

    Those authors do (incorrectly) claim that the sender doesn't spend energy, it's really their main point.

  18. energy doesn't travel with information? that doesn't make any sense. information travels via energy. it's called modulation. you vary some aspect of the carrier energy (amplitude, frequency, phase) to encode the information.

  19. Hi All,

    I'm posting a comment on behalf of Achim Kempf, on of the paper's authors

    "Great to see all this interest!

    Lubos wrote: "Those authors do (incorrectly) claim that the sender doesn't spend energy, it's really their main point."

    Actually, we don't claim any such thing. Of course both Alice and Bob invest energy. The point is that Bob receives no energy from Alice.

    On other questions:

    Yes of course, the energy is conserved.

    Yes, classically, Alice can communicate binary messages to Bob by either doing or not doing some action they agreed upon. This implies that, sometimes, Alice sends a message to Bob without sending him energy. But this also means that, sometimes, Alice has has to do something. If not, i.e., if Alice could only send the "no action" message then Bob would know the message beforehand so no info would be transmitted.

    Now the assumption has been that this implies that Alice in those "doing something" cases needs to transmit energy to Bob. This would mean that the continued operation of their communication protocol requires energy transmission from Alice to Bob.

    Except, we showed that, in certain circumstances, Alice can perform an action that signals a message to Bob without energy traveling from Alice to Bob."

  20. To clear things a little. I do not understand the whole theory beside it, but is seems to me they state that:

    0. _massless_ field is used. For 3+1D Minkowski space it has correlation only on null lightcone. 2n +1D Minkowski spacetime is different.
    1. information is transfered within lightcone ( null or timelike separation) in 2n +1D dimension
    2. the same effect is possible in _curved_ 3+1d Minkowski space.
    3. physical effect for "recieving" signal is -- which is basically Casimir force.
    4. modulation ( within timelike lightcone) of vacuum states ( basically changes of state of standing waves between two plates in Casimir like settings) is used to send information between sender and receiver. Omitting short "instabilities" during move only "steady state" of steading waves is used for signaling.
    4. Receiver looks for changes of state of his own device coupled to the vacuum, sender changes state of his own device coupled to the vacuum. Changes of state of receiver and sender has to be correlated ( due to given schedule?)?
    5. energy is used to change state of devices both in receiver and sender device's settings, but energy does not flow between them.

    rest is calculation...

  21. If we can send information without energy, what prevents this information exchange from propagating faster than the speed of light?

  22. Arun: The points are timelike separated, not spacelike separated.

  23. Concerning Dr Kempf's reply to my objections. Well, it does look like - as someone has pointed out - that he suggests that if sending "0" means to do nothing, then one may send "0" without any expenditure of energy.

    But if one knows what the digit is, namely that it's "0", then the amount of information that is sent is zero. Information is only being sent if one doesn't know in advance what he will receive. That's only possible if there's a possibility that one does something different, and needs to spend energy to do something else.

    And the claim that Alice may do something but send no energy? It is not possible. At least, everyone who "does something" is creating some motion, so he emits at least gravitational waves.

    But they talk about the coupling of the transmission power with the massless field. That's only possible when they interact with each other - otherwise the massless field doesn't care about the transmission power. In practice, it means that the "transmission power" contains electric charges (something interacting with the massless field). And "coupling them" means to change something about these charges. But changing something about the speed etc. of charges means to send the electromagnetic (or other massless) waves.

    Whatever I read strengthens the interpretation that they talk about a rather normal sending of the information through a classical antenna, not a terrible efficient one. They just overlook or deny the energy carried by the electromagnetic waves leaving the antenna, and cover these very mundane processes by lots of nonsensically fancy, quantum information talk - even though this has really nothing to do with quantum information at all.

  24. Lubos,

    You're right, but that isn't what they're saying in the paper. There is a (local) exchange of energy between the field and the detector (explicitly present in the Hamiltonian) and there is also a propagation of energy in the field, it's just that the energy doesn't entirely propagate together with the information. It's a massless field, the energy ('real quanta') propagates on the lightcome, while the correlations they talk about are inside the lightcone (timelike). See the 3rd paragraph page 3 left ("Remarkably,...") about the question of where the real quanta are. Best,


  25. Bee,

    "Yes, good point. You can of course send information without it being accompanied by energy, and you don't even need quantum mechanics for this. We can just agree that if you don't show up by 8pm, we will meet later at the movies, so then your non-appearance has sent me information without any energy. But we previously had to agree on some code for this. The quantum information people have all kinds of protocols for what exactly they mean with information transfer, but unfortunately I'm not very familiar with them. Whenever you get a message by the absence of a signal though, you first must have agreed on what is being done."

    I don't understand your point here. Or maybe I don't understand the experiment.

    Blocking and unblocking idler1 causes the interference pattern at the signal detector to appear and disappear. In neither case is any photon from idler1 go to the signal detector.

    Its more like if my cousin shows up at the restaurant at 8pm then you somehow know that I will show up at the movie theater at 8pm despite the fact that you are nowhere near the restaurant and can't know where my cousin is.

    Which way information is created with the creation of the two idler photons. That information is destroyed when the idler photons are combined. In no case does any idler photon ever go to the signal detector yet a signal is sent by their distant recombination.

    Any observer could see the Interference pattern appearing and disappearing. From that they could see that a message is being transmitted even if they did not know the code.

  26. Dear Bee, let me expand my comment. In undergraduate physics we learn the following for wave velocity, group velocity and the speed of light for electromagnetic radiation.

    V_wave * V_group = c * c

    We are then assured that V_group, the speed at which energy propagates, is always less than c; and since information transfer requires energy, no information transfer can happen faster than the speed of light.

    Now it seems the relation between information transfer and energy transfer is broken; information transfer can happen without energy transfer. Suddenly that assurance given to undergraduates seems to be on shaky ground. Maybe the case described in this paper is a very special circumstance; or maybe the reason we haven't detected extra-solar civilizations is because we haven't mastered superluminal information transfer :)


  27. @Lubos "But if one knows what the digit is, namely that it's "0", then the amount of information that is sent is zero. Information is only being sent if one doesn't know in advance what he will receive. " - no, because You do not set enough context in the protocol. For send some portion of information, You need some kind of code, protocol etc. The simplest protocol is as follows:
    -synchronise clocks
    -agree on some time T in the future of both Alice and Bob.
    -separate Alice and Bob, still measuring time.
    -if at time T thee is no signal from Bob Alice assume that message is "A"
    -if at time T there is signal from Bob, Alice assume that message is "B"

    It is clearly obvious that:
    1. if there is no signal at time T, Alice obtained information "A", and before that she do not know if Bob do not send different message ( "B") which he can do!

    So - information was sent, no exchange of energy or mass etc. Alice and Bob may continue communication at times T1, T2, ... Tn

  28. Sabine, I haven't seen any evidence that the propagation of information may be decoupled from the propagation of energy.

    In odd spacetime dimensions, the propagator is nonzero in the timelike interior of the light cone which means that both information *and* energy created at the source are initially moving slower than light.

    It makes no sense to say that this propagator only means something for the information but nothing for the energy. It means the same thing for the energy, too, and perhaps *primarily* for the energy.

    For the timescales shorter than or comparable to the inverse frequency, the initial impulse just spreads mostly slower than light - because the strong Huygens' principle isn't right. That's a totally classical statement that strongly modifies the propagation of the electromagnetic fields at small enough lags. At much longer lags, relatively to the inverse frequency, much of the propagator is concentrated near the light cone, anyway, and one may see that the information moves mostly by the speed of light, too.

    So this is just a reiteration of the very well-known classical point about the modified/failing Huygens' principle in 3D, with some illogical interpretations - interpretations treating energy and information asymmetrically, without any justification - added on top of that.

  29. Dear fiksacie, for A and B to agree about the conventions, codes, and protocols, they need to send even more information - and more energy - than without it. So whatever you write, when interpreted rationally, only *strengthens* my self-evidently correct point that one can't send information without sending energy.

  30. fiksacie, so if Alice and Bob get together and exchange information then that means that Alice and Bob can communicate without sending information. Hmm, I think I see a flaw in your reasoning.

    Back to the paper. Information always refers to some aspect of the physical world, be it a bit in a computer or a quantum state vector. It is meaningless to talk of information with no physical representation, as if it is "in the ether". If information passes from Alice and appears with Bob sometime later then during the intervening period it has been stored and transmitted using some physical medium. If that is not energy then I want to know what it is, because it is certainly not nothing.

    That's my take on it. I would love the authors to state on which physical medium the information is transmitted if it is not energy. Are we talking telepathy here?

  31. @Libos, @Thomas - they agreed on protocol. So it is true, that not all information is sent without energy. But as they have protocol based on local observation, and local time measuring - some information may be sent without energy.

    But this is not the aim of the article we disputing about - it was just loose co-comment to Your comment.

  32. @Andrew Thomas - in the base paper, they do not say that, they have much more complicated systems. Of course I know I may be completely wrong.

    But for simple case, consider this: Casimir like settings - two plates, and standing vacuum waves between them. In classical setting You have to propel this system by transferring energy in order to have standing waves running. But in quantum case, vacuum oscillations are used so You do not transfer any energy into system, and they are still present. For such system of "Casimir mirrors" only some frequencies are possible, between plates.

    You may signalling by changing geometry of this settings, and when You change distance between "Casimir mirrors" - state of standing waves - changes.

    Of course when You change distance between plates You have to fight with radiation pressure on both sides. But both sender and receiver system do not use "vacuum states" during "geometry changes" for signalling! Suppose they only measures state after that, when geometry off the system is static one. And they use for such purposes, given in advance time schedule, so they do not have to measure if other partner finished his part of the operation. They simply measure local state of the vacuum on his end of the system, at certain moments T_i And they use some code/protocol for which information is described by for say - value of the length of the maximum ( or the length of the most probable) standing wave.

    They uses only "steady states" when standing waves are in stationary state. So for information transfer no energy is transferred from sender to receiver ( but both parties has to invest energy in change of geometry of theirs systems ).

    It probably do not work at all ;-) so they have to build in the article much more complicated situation. but I believe that very broad idea ff the situation is as I described here

  33. Another comment on behalf of Achim

    "In reply to Lubos' comments:

    Lubos, have a look at the paper. You'll find that we explain that in most dimensions information and energy transport cannot be cleanly separated because energy leaks into the lightcone. And that is why we explain at great length that in 1+1 dimensions one can cleanly separate info and energy transport. That's because in 1+1 dimensions, no energy propagates inside the lightcone. The reason why in 1+1 dimensions no energy propagates inside the lightcone is also explained in the paper. "

  34. Achim, the massless propagator is constant in the time-like region in 1+1 dimensions but aside from simplicity and integrability, it changes nothing about the general ways how energy and information propagate. Only the quantitative profiles are different than in other dimensions.

    To send information, one still has to perturb the field at the initial place in a time-dependent way, and this time dependence gives rise to energy density. That energy density propagates superluminally, along the light cone only, but so does the information.

    Whether the field jumps along the light cones depends on the initial conditions. Classically, one may always change the answer by adding a function f(xPLUS) or f(xMINUS) to the fields.

    The main technical point that makes both of these configurations equally good is that there are *no* superselection sectors in 1+1 dimensions, as Sidney Coleman proved. See also his "There are no Goldstone bosons in two-dimensions". That's why your would-be recipient of information inside the light cone can't really compare the value of the field with the "right" value field at infinity - the latter doesn't exist due to the large quantum fluctuations (caused by the low-dimension large infrared effects).

    So there are different exceptions - like the propagators' being zero only on the light cone, or inside, and also some special IR effects in low enough dimensions, but one has to be careful about *all* the modifications that these special conditions mean for a physical situation, and when he does it right, he will still see that it's impossible to propagate information without an energy carrier.

  35. The transport of information is in no way a "calculation" operation because there is no processing of information. Only the write operation to the destination should be considered a computing operation requiring 1) information storage 2) modification of the stored information. Reading is only a epistemological need to be able to claim that a storage of information does really exist.

    The only way to make a "non-energetic" calculation, considering the theorem of Landauer, is the utilisation, like Brassard suggests, of reversible doors like Toffoli one. By cons, this possibility does not imply the falsity of Landauer's theorem as Brassard presumes (Laval, 2007) but that it is probably impossible to store information in space without use energy.

    Indeed, if it is impossible to conceive a reversible computing without storage and conservation of the original information as in the Toffoli doors and that Landauer's theorem is true, then any information storage operation in space consumes energy.

    That said, if the mechanism described here can be used to store information in space by applying the principle of the delay lines memory then this is probably wrong.

  36. In absence of relationship a binary bit has no significance. Only as a part of a larger, meta-level framework does it have any real magnitude. As with energy, information in measured in a change of state.
    For example, Bob is in a dark room with a light proof window that can be opened to view some pleasant terrestrial vista. Alice calls Bob on a cell phone and says, “Open your window.” Bob opens his window and, by previous agreement, if it is daylight out, he writes down a “1” and, if dark out, he writes “0”. Communication would thus be possible at considerably less than light speed.

    So when does the change of state take place and does energy originating from Alice drive it?

  37. Another comment from Achim:


    Please read the paper and then let us know in which step you believe we went wrong.

  38. ppnl,

    Sorry, I thought you had meant information transfer from the sender. In the case you think about, I don't see how this can work without energy transmission. Think of a double-slit where you either block or unblock the second slit, thereby changing the interference pattern on some location on the screen. The reason you get this change is that you are blocking out part of the wave which would otherwise interfere with the other part of the wave. This must be a local effect and there must be an energy flow, or absence of that flow respectively, related to this. As has been pointed out above already you can't make a signal just with one bit, you need to be able to switch, so you necessarily need both, presence and absence of the interference pattern. Best,


  39. Another comment from Achim

    Lubos, regarding your intuition, notice that it is also possible to send energy from Alice to Bob without the energy actually traveling between Alice and Bob. It is called quantum energy teleportation:

  40. Achim, the interpretative claim in Hotta's paper is more or less equivalent to yours and it is equally incorrect, too.

    The particular mistakes in your paper are all the sentences that visibly don't follow from the surrounding technical material.

    From a term's scaling like O(lambda_A*lambda_B), it doesn't follow that no quanta are being exchanged, as you claim on page 3, for example.

    It isn't true that in 1+1 dimensions, one can copy the same information - regardless of the weakness of the signal that was sent - arbitrarily many times just because the propagator is constant. I've already discussed that - the IR noise one has to suppress is correspondingly large, too.

    At the end, there is a minimum amount of energy one needs to transmit a bit at a certain characteristic frequency, E=O(f), and your paper just doesn't contain any evidence to the contrary.


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