Related papers: Has the Born rule been proven?

In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a natural transformation of functors. In…

Complex phase factors are viewed not only as redundancies of the quantum formalism but instead as remnants of unitary transformations under which the probabilistic properties of observables are invariant. It is postulated that a quantum…

This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.

An technically interesting proof of a known theorem.

We compare and contrast two distinct approaches to understanding the Born rule in de Broglie-Bohm pilot-wave theory, one based on dynamical relaxation over time (advocated by this author and collaborators) and the other based on typicality…

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.

This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)

This is an exposition of Gauss's proof of Descartes's rule of signs.

We have recently developed a new understanding of probability in quantum gravity. In this paper we provide an overview of this new approach and its implications. Adopting the de Broglie-Bohm pilot-wave formulation of quantum physics, we…

The Rev. Dodgson's determinant condensation rule is given a bijective proof.

Everett's Relative State Interpretation has gained increasing interest due to the progress of understanding the role of decoherence. In order to fulfill its promise as a realistic description of the physical world, two postulates are…

Selected examples of possible origins of power-law distributions are presented.

In a recent paper [1], it has been claimed that the outcomes of a quantum coin toss which is idealized as an infinite binary sequence is 1-random. We also defend the correctness of this claim and assert that the outcomes of quantum…

This paper has been withdrawn due to submission of subsequent versions as a new preprint

A review by A. Peres [quant-ph/0205076] appears recently. It is difficult to add something to such kind of fundamental themes, but here is briefly presented some ideas about challenges of the no-cloning theorem and imaginary modifications…

The Born rule asserts the probability distribution of eigenstates observed in unbiased quantum measurements, but the reason it holds remains elusive. This manuscript discusses how the Born rule might be explained by Schrodinger equation…

In this paper we obtain some possibilistic variants of the probabilistic laws of large numbers, different from those obtained by other authors, but very natural extensions of the corresponding ones in probability theory. Our results are…

There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…

It is shown that Darwiche and Pearl's postulates imply an interesting property, not noticed by the authors.

We show that probabilities of results of all possible measurements performing on a quantum system depend on the system's state only through its density matrix. Therefore all experimentally available information about the state contains in…