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In this essay, I review the importance of languages in the study of reality, following the well-known aphorisms by Galilei, Bohr and many others. The emphasis on these aspects helps us to understand that it is not meaningful to ask if the…
It is regrettable that the quantum length of an object is rarely if ever discussed, because it provides an ideal pedagogical paradigm for understanding how a physicist uses classical intuition to define quantum properties and how such…
Two philosophical applications of the concept of program-size complexity are discussed. First, we consider the light program-size complexity sheds on whether mathematics is invented or discovered, i.e., is empirical or is a priori. Second,…
Nature has found one method of organizing living matter, but maybe other options exist -- not yet discovered -- on how to create life. To study the life "as it could be" is the objective of an interdisciplinary field called Artificial Life…
We show that in a quantum measurement, the preferred basis is determined by the interaction between the apparatus and the quantum system, instead of by the environment. This interaction entangles three degrees of freedom, one system degree…
Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…
The possibility to describe the laws of the Universe in a computational way seems to be correlated to a principle that the density of information is bounded. This principle, that is dual to that of a finite velocity of information, has…
In this thesis we study continuously observed open quantum systems from the point of view of quantum filtering theory. The conditioned state of the open system obeys a non-commutative or quantum analogue of the Kushner-Stratonovich equation…
A contemporary physicist would be hard put to agree entirely with the author of a 1959 textbook on quantum mechanics, who wrote: "A second simple, one-dimensional system, somewhat divorced from reality but illustrative of the principles of…
The possibility of a quantum system to exhibit properties that are akin to both the classically held notions of being a particle and a wave, is one of the most intriguing aspects of the quantum description of nature. These aspects have been…
While quantum computers promise significant advantages, the complexity of quantum algorithms remains a major technological obstacle. We have developed and demonstrated an architecture-independent technique that simplifies adding control…
A physical system is determined by a finite set of initial conditions and "laws" represented by equations. The system is computable if we can solve the equations in all instances using a "finite body of mathematical knowledge". In this…
We address the impossibility of achieving exact time reversal in a system with many degrees of freedom. This is a particular example of the difficult task of "aiming" an initial classical state so as to become a specific final state. We…
The set of correlations between particles in multipartite quantum systems is larger than those in classical systems. Nevertheless, it is subject to restrictions by the underlying quantum theory. In order to better understand the structure…
Data compression is a ubiquitous aspect of modern information technology, and the advent of quantum information raises the question of what types of compression are feasible for quantum data, where it is especially relevant given the…
In this work we initiate the question of whether quantum devices can provide us with an almost perfect source of classical randomness, and more generally, suffice for classical cryptographic tasks, such as encryption. Indeed, it is well…
We explore the structure of multipartite quantum systems which are entangled in multiple degrees of freedom. We find necessary and sufficient conditions for the characterization of tripartite systems and necessary conditions for any number…
Can certain degrees of freedom of a closed physical system, described by a time-independent Hamiltonian, become more and more classical as they evolve from some state? This question is important because our universe seems to have done just…
Why are the laws of physics formulated in terms of complex Hilbert spaces? Are there natural and consistent modifications of quantum theory that could be tested experimentally? This book chapter gives a self-contained and accessible summary…
We describe here, for the first time, a lower bound on the total number of fundamental constants required for a mathematical description of our physical universe to be complete. The answer is shown to be one. The formal arithmetized…