Decoupling of Information Propagation from Energy Propagation
Jonsson, Robert H.
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Information and energy are concepts central to our understanding of nature. Their relevance, in physics, ranges from fundamental physics, e.g., in black hole physics, all the way to future quantum computing technology. This thesis investigates how information and energy propagate in quantum fields. The main result is that in massless fields the propagation of information can decouple from the propagation of energy partially and, under special circumstances, even completely. It has been known that in general curved spacetimes, and also in odd-dimensional Minkowski space, signals can propagate slower than light even in a massless field. Here it is shown that the energy-to-information ratio of these classical timelike signals can approach zero. The extreme case is marked by two-dimensional Minkowski space. In this case, timelike signals reach arbitrarily far into the future lightcone, without diluting, and they carry no energy at all. Instead, the energy cost associated with the detection of energyless signals has to be provided by the receiver, much as in a collect call. Technically, sender and receiver are modelled as basic first-quantized systems coupling locally to the relativistic quantum field, i.e., as Unruh-DeWitt particle detectors. This gives rise to a standard quantum channel from the sender to the receiver. Thus, the tools of quantum information can be applied to investigate the combined impact of relativistic and quantum effects on the propagation of information. In the perturbative regime, signals analogous to phase modulation are shown to over- come signals analogous to amplitude modulation: It is shown that the sender has to prepare superpositions of eigenstates, to achieve signalling effects at leading order. Signals from pure energy eigenstates are subdominant, and only appear in next-to-leading order. The classical channel capacities resulting from optimal signalling states are calculated. Analyzing the energy injected into the field by the sender, it is shown that signals reach further in spacetime than the energy radiated by the sender, both for timelike, as well as for lightlike signals. Instead, the energy budget is balanced by the energy that the receiver has to provide when decoupling the detector from the field. This switching cost is particularly sensitive to timelike signals. Timelike signals are also demonstrated to occur between harmonic oscillators coupling to the field inside a cavity. This model could be instrumental for future research, because it can be treated non-perturbatively using Gaussian methods. Such numerical calculations only take into account a finite number of field modes. It is shown that relativistic properties of the field can still be resolved reliably, because the number of necessary modes scales with the desired accuracy, namely following a power law.