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The existence of a minimal observable length has long been suggested in quantum gravity as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal length as a minimal uncertainty in position measurements. Here we study in full detail the quantum mechanical structure(More)
In most inflationary models, space-time inflated to the extent that modes of cosmological size originated as modes of wavelengths at least several orders of magnitude smaller than the Planck length. Recent studies confirmed that, therefore, inflationary predictions for the cosmic microwave background perturbations are generally sensitive to what is assumed(More)
We show that the theory of operator quantum error correction can be naturally generalized by allowing constraints not only on states but also on observables. The resulting theory describes the correction of algebras of observables (and may therefore suitably be called "operator algebra quantum error correction"). In particular, the approach provides a(More)
The existence of a natural ultraviolet cutoff at the Planck scale is widely expected. In a previous Letter, it has been proposed to model this cutoff as an information density bound by utilizing suitably generalized methods from the mathematical theory of communication. Here, we prove the mathematical conjectures that were made in this Letter.
Studies in string theory and quantum gravity suggest the existence of a finite lower limit ∆x 0 to the possible resolution of distances, at the latest on the scale of the Planck length of 10 −35 m. Within the framework of the euclidean path integral we explicitly show ultraviolet regularisation in field theory through this short distance structure. Both(More)
Quantum mechanics ordinarily describes particles as being pointlike, in the sense that the uncertainty ∆x can, in principle, be made arbitrarily small. It has been shown that suitable correction terms to the canonical commutation relations induce a finite lower bound to spatial localisation. Here, we per-turbatively calculate the corrections to the energy(More)