Under the Extended Uncertainty Principle, position variance saturates, and the entanglement entropy of harmonic chains and massless scalar fields saturates to a finite value with a discrete, evenly gapped entanglement spectrum.
Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
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abstract
We introduce a novel measure to quantify the non-Gaussian character of a quantum state: the quantum relative entropy between the state under examination and a reference Gaussian state. We analyze in details the properties of our measure and illustrate its relationships with relevant quantities in quantum information as the Holevo bound and the conditional entropy; in particular a necessary condition for the Gaussian character of a quantum channel is also derived. The evolution of non-Gaussianity (nonG) is analyzedfor quantum states undergoing conditional Gaussification towards twin-beam and de-Gaussification driven by Kerr interaction. Our analysis allows to assess nonG as a resource for quantum information and, in turn, to evaluate the performances of Gaussification and de-Gaussification protocols.
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Resolution of Infrared Entanglement Divergences via the Extended Uncertainty Principle
Under the Extended Uncertainty Principle, position variance saturates, and the entanglement entropy of harmonic chains and massless scalar fields saturates to a finite value with a discrete, evenly gapped entanglement spectrum.