Generally speaking we have done a fairly decent job of not thinking too linearly. Eg. Moore's Law, Kurzweil's Accelerating Returns Law, Engelbart's Law...to name a few.
"The key problem is how to de-financialize real economy companies, and to find ways
that value creation activities (in both the financial sector and real economy) are
rewarded over value extraction activities. This will entail both finding and supporting
sources of finance that provide long-term committed patient capital, but also specific
policy mechanisms that limit the power of large shareholders, which has allowed
‘trading’ to be rewarded over ‘investment’ and also caused innovation-led growth (a
result of a collective process) to lead to a less collective, less equitable, highly unstable
economic structure." - M. Mazzucato (2013)
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography.
