Godel's proofs of the incompleteness theorems are frequently discussed in the context of constructive or nitary viewpoint. Godel showed a concrete independent statement of arithmetic and the proof does not contain any transcendental argument. On the other hand, the completeness theorem asserts that a sentence is not derivable from a theory if and only if there exists a model of the theory whi...

We introduce the telescopic relative entropy (TRE), which is a new regularisation of the relative entropy related to smoothing, to overcome the problem that the relative entropy between pure states is either zero or infinity and therefore useless as a distance measure in this case. We study basic properties of this quantity, and find interesting relationships between the TRE and the trace norm ...

In this paper we categorize the coherence traac in update-based protocols and show that, for most applications , more than 90% of all updates generated by the protocol are unnecessary. We identify application characteristics that generate useless update traac, and compare the isolated and combined eeects of several software and hardware techniques for eliminating useless updates. These techniqu...

Abstract Among the known resources of quantum metrology, one most practical and efficient is squeezing. Squeezed states atoms light improve sensing phase, magnetic field, polarization, mechanical displacement. They promise to considerably increase signal-to-noise ratio in imaging spectroscopy, are already used real-life gravitational-wave detectors. But despite being more robust than other stat...

In this work, we will identify the existence of “rough dependence on initial conditions” in atmospheric phenomena, a concept which is a problem for weather analysis and forecasting. Typically, two initially similar atmospheric states will diverge slowly over time such that forecasting the weather using the Navier-Stokes equations is useless after some characteristic time scale. With rough depen...