Information Transmission Without Energy Exchange

Abstract

We show that it is possible to use a massless field in the vacuum to communicate in such a way that the signal travels arbitrarily slower than the speed of light and such that no energy is transmitted from the sender to the receiver. Instead, the receiver has to supply a signal-dependent amount of work to switch his detector on and off. Because of that, this kind of communication without energy exchange may be called "Quantum Collect Calling". This type of communication is related to Casimir-like interactions and it is made possible by dimension -and curvature-dependent subtleties of Huygens' principle.Communication by means of massless quantum fields is normally discussed in terms of the exchange of field quanta. Typically, a sender emits photons -which carry energy along null-geodesics-that are then absorbed by a receiver. The receiver has to intercept the beam of light, or he misses the signal. In this letter we introduce a method of communication via massless quantum fields which breaks with each point of the just mentioned intuitive understanding: 1) No emission or absorption of real quanta is necessary; 2) the information flow need not be carried by an energy flow; and 3) the information flow can be arbitrarily slower than light, in spite of the field being massless.The fact that waves of massless fields propagate at exactly the speed of light is merely a peculiar feature of n + 1D Minkowski spacetime, for odd n ≥ 3. When there is generic curvature, or when the spatial dimension is even, then waves of massless fields propagate both on as well as inside the lightcone [1,2,8]. Here, we translate this classical wave phenomenon into quantum field theory (QFT) and analyze the implications for quantum communication.Surprisingly, when applied to QFT, we find that the resulting signal transmission effects appear already at the leading order in perturbation theory. These are not emission and absorption processes of real photons, which only appear at subleading order. Indeed, we find that slowerthan-light quantum signals do not require the transmission of energy from the sender to the receiver. Instead -much as for a collect call-the receiver has to provide energy for the detection of the signal.The strong Huygens' principle in QFT.-The Green's functions of the massless Klein-Gordon field in 3+1D Minkowski space have support only on the lightcone. Hence, any disturbances of the field propagate strictly along null geodesics. This classical phenomenon is called the strong Huygens' principle [1,2].In QFT, communication via the field is possible if and only if the commutator between the field at two events does not vanish [3][4][5][6][7]. The commutator is given by the Green's function [φ(x, t 1 ), φ(y, t 2 )] = iG(x, t 1 , y, t 2 )1 1, where G = G adv − G ret ; thus the commutator always vanishes outside the lightcone. The strong Huygens' principle therefore manifests itself in QFT through the commutator of the field: In 3+1D Minkowski space, the commutator is only supported on the lightcone. In 1+1D and 2+1D, the comm...

Transmission of quantum information through quantum fields

“…Namely, recall that the strong Huygens principle states that the massless field's radiation Green's function (and hence the expectation of the field commutator in the quantum case) only has support between lightlike separated events [2], and hence communication between observers via this quantum field is only possible if they are in null separation. While the implications of this fact have previously been studied in great detail for classical communication protocols [41][42][43][44][45], the work presented here is the first time that the effects of the strong Huygens principle have been studied in the context of quantum communication.…”

Regularized calculation of the retarded Green function in a Schwarzschild spacetime

“…The approximation becomes worse the further the points are from each other in the sense of large coordinate increments (i.e. large |t − t |, |r − r | and/or γ) 3 . The aim is to match the calculation of V (x, x ) via (4), with the sums truncated, to the mode-sum calculation via (3), also with the sum truncated, in a region where both approximations are accurate enough (i.e., the truncation error is smaller than a desired accuracy).…”

Precise space–time positioning for entanglement harvesting

“…Inter-detector separation and detector switching can be partitioned into two regimes: lightlike contact, whereby real quanta can be exchanged, and spacelike separation, whereby they cannot be exchanged. Notice that it is possible that the two detectors communicate when they are in timelike contact even though energy does not necessarily flow from Alice to Bob [22][23][24][25]. In the spacetime diagram in figure 1, we present the possible cases of relative positioning of Aliceʼs and Bobʼs detectors, following the same conventions as in [23,26].…”