16 Matching Annotations
  1. Jul 2019
    1. unitary operator is a surjective bounded operator

      Why must unitary operator only be surjective? Why not bijective?

  2. Mar 2019
    1. Special Complexity Zoo Exhibit: Classes of Quantum States and Probability Distributions 24 classes and counting! A whole new phylum of the Complexity kingdom has recently been identified. This phylum consists of classes, not of problems or languages, but of quantum states and probability distributions. Well, actually, infinite families of states and distributions, one for each number of bits n. Admittedly, computer scientists have been talking about the complexity of sampling from probability distributions for years, but they haven't tended to organize those distributions into classes designated by inscrutable sequences of capital letters. This needs to change.
  3. Jan 2019
    1. The new experiment shows that, in a quantum world, two people can end up disagreeing about a seemingly irrefutable result, such as the outcome of a coin toss, suggesting something is amiss with the assumptions we make about quantum reality.
    2. Frauchiger and Renner came up with their thought experiment, which is an extension of something the physicist Eugene Wigner first dreamed up in the 1960s.
  4. Nov 2018
  5. Aug 2018
    1. Hegel believed that history culminated in an absolute moment - a moment in which a final, rational form of society and state became victorious.

      and probably not a bad outcome in an earlier era that thought of things in terms of clockwork and lacked the ideas of quantum theory and its attendant uncertainties.

  6. May 2018
  7. Apr 2018
    1. “We often discussed his notions on objective reality. I recall that during one walk Einstein suddenly stopped, turned to me and asked whether I really believed that the moon exists only when I look at it.”
  8. Mar 2018
  9. Feb 2018
  10. Apr 2016
    1. The notion that counting more shapes in the sky will reveal more details of the Big Bang is implied in a central principle of quantum physics known as “unitarity.” Unitarity dictates that the probabilities of all possible quantum states of the universe must add up to one, now and forever; thus, information, which is stored in quantum states, can never be lost — only scrambled. This means that all information about the birth of the cosmos remains encoded in its present state, and the more precisely cosmologists know the latter, the more they can learn about the former.
  11. Dec 2015
    1. this week’s announcement by Google that a machine made by a Canadian company, D-Wave Systems, which is marketed as “the world’s first commercial quantum computer”, had shown spectacular speed gains over conventional computers. “For a specific, carefully crafted proof-of-concept problem,” Google’s Hartmut Neven reported, “we achieved a 100-million-fold speed-up.”
  12. Oct 2015
    1. the strongest evidence yet to support the most fundamental claims of the theory of quantum mechanics about the existence of an odd world formed by a fabric of subatomic particles, where matter does not take form until it is observed and time runs backward as well as forward.
  13. Feb 2014
    1. The mathematics of almost all eigenvalue problems encountered in wave physics is essentially the same, but the richest source of such problems is quantum mechanics, where the eigenvalues are the energies of stationary states ("levels"), rather than frequencies as in acoustics or optics, and the operator is the hamiltonian.