Related papers: Kolmogorov Algorithmic Complexity and its Probabil…
Bringing gravity into a quantum-mechanical framework is likely the most profound remaining problem in fundamental physics. The "unitarity crisis" for black hole evolution appears to be a key facet of this problem, whose resolution will…
We prove the first meta-complexity characterization of a quantum cryptographic primitive. We show that one-way puzzles exist if and only if there is some quantum samplable distribution of binary strings over which it is hard to approximate…
These lectures discuss an S-matrix approach to quantum gravity, and its relation to more local spacetime approaches. Prominent among the problems of quantum gravity are those of unitarity and observables. In a unitary theory with solutions…
Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits' complexity…
This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of…
This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…
We study how meaningful physical predictions can arise in nonperturbative quantum gravity in a closed Lorentzian universe. In such settings, recent developments suggest that the quantum gravitational Hilbert space is one-dimensional and…
In a recent article, Khrennikov claims that a particular theorem about agreement between quantum measurement results poses a problem for the interpretation of quantum mechanics known as QBism. Considering the basic setup of that theorem in…
Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory…
Computer simulations allow us to explore non-perturbative phenomena in physics. This has the potential to help us understand quantum gravity. Finding a theory of quantum gravity is a hard problem, but in the last decades many promising and…
We investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods. The algebraic tools are similar to ones used in constructing topological quantum field theories.The algebraic tools…
Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation and choice of gauges are pointed out.…
In the mentioned paper we presented results of the estimation of Kolmogorov complexity of sequences of random numbers generated in a famous Bell's experiment, aimed to study the security of QKD. We focused on series of time differences…
General relativity, despite its profound successes, fails as a complete theory due to presence of singularities. While it is widely believed that quantum gravity has the potential to be a complete theory, in which spacetime consistently…
The general problems of three-dimensional quantum gravity are recatitulated here, putting the emphasis on the mathematical problems of defining the measure of the path integral over all three-dimensional metrics.This work should be viewed…
Starting from a new understanding of the vacuum energy problem based on the combination of the phase space regularization and the holographic bound, we argue that quantum gravity should be understood as gravitized quantum theory, that is,…
An approach to quantization of fields and gravity based on the De Donder-Weyl covariant Hamiltonian formalism is outlined. It leads to a hypercomplex extension of quantum mechanics in which the algebra of complex numbers is replaced by the…
The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…
In seeking to arrive at a theory of ``quantum gravity'', one faces several choices among alternative approaches. I list some of these ``forks in the road'' and offer reasons for taking one alternative over the other. In particular, I…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…