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Quantum information in electromagnetism and gravity DeLisle, Colby L.


The electromagnetic and gravitational fields transfer information between physical systems. This work is an attempt to better understand how matter systems communicate quantum information with one another using these fields, and also how quantum information about matter is broadcast into the fields themselves. We study the former process in Part I and the latter in Part II, by answering two distinct but related questions. Part I of this work studies experimental proposals to observe gravity-induced quantum entanglement between matter systems. If these are successful, it can be argued that they would be the first experimental witness of a quan- tum superposition of space-time geometries, although this interpretation of the proposals has been the subject of vigorous debate. To address this, we first utilize the “quantum action principle” to quantize the electromagnetic and (linearized) gravitational fields. We find that for the quantization to be self-consistent, physical quantum states in the theory must be gauge- and diffeomorphism-invariant. We then show that these constraints are the root cause of the confusion surrounding the proposed gravity-induced en- tanglement experiments. A deeper understanding, however, of how these constraints change when assigning quantum states to different hypersur- faces in space-time provides a satisfying resolution to the debate over the experimental proposals. We conclude that if gravity-induced entanglement is observed, it should be interpreted as experimental evidence in favor of the quantum nature of space-time. Part II then addresses the quantum information content of low energy “soft” radiation. We first show that whether matter particles emit such radiation depends entirely upon the past and future boundaries of the worldlines they follow. This observation explains all tree-level “soft theorems” in both electromagnetism and gravity. We then quantize the electromagnetic and gravitational fields asymptotically, at null infinity. Again, the quantization compels us to ensure physical states are invariant under gauge transforma- tions and diffeomorphisms which persist in the asymptotic limit. Invariance under these “large” transformations fully constrains the state of the leading- order soft radiation, meaning that this radiation cannot carry quantum in- formation. Finally, we illustrate how our construction also avoids infrared divergences when predicting decoherence rates in a model interferometry experiment.

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