Related papers: The algorithmic randomness of quantum measurements

Quantum random number generator harnesses the power of quantum mechanics to generate true random numbers, making it valuable for various scientific applications. However, real-world devices often suffer from imperfections that can undermine…

Within quantum mechanics it is possible to assign a probability to the chance that a measurement has been made at a specific time t. However, the interpretation of such a probability is far from clear. We argue that a recent measuring…

Randomness is intrinsic to quantum mechanics; the outcome of a measurement on a quantum state is a random variable. This feature has been applied to randomness certification, where one party must decide whether the data they receive is…

Randomness is an indispensable resource in modern science and information technology. Fortunately, an experimentally simple procedure exists to generate randomness with well-characterized devices: measuring a quantum system in a basis…

In this Letter, we strengthen and extend the connection between simulation and estimation to exploit simulation routines that do not exactly compute the probability of experimental data, known as the likelihood function. Rather, we provide…

The concept of randomness plays an important role in many disciplines. On one hand, the question of whether random processes exist is fundamental for our understanding of nature. On the other hand, randomness is a resource for cryptography,…

The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…

The fundamental principles of quantum mechanics, such as its probabilistic nature, allow for the theoretical ability of quantum computers to generate statistically random numbers, as opposed to classical computers which are only able to…

This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…

When an experimentalist measures a time series of qubits, the outcomes generate a classical stochastic process. We show that measurement induces high complexity in these processes in two specific senses: they are inherently unpredictable…

Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural…

We study the optimization of any quantum process by minimizing the "randomness" in the measurement result at the output of that quantum process. We conceptualize and propose a measure of such randomness and inquire whether an optimization…

We extend algorithmic conservation inequalities to probability measures. The amount of self information of a probability measure cannot increase when submitted to randomized processing. This includes (potentially non-computable) measures…

We study the randomness properties of reals with respect to arbitrary probability measures on Cantor space. We show that every non-computable real is non-trivially random with respect to some measure. The probability measures constructed in…

We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense…

As computability implies value definiteness, certain sequences of quantum outcomes cannot be computable.

A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…

Irreversibility in quantum measurements is considered from the point of quantum information theory. For that purpose the information transfer between the measured object S and measuring system O is analyzed. It's found that due to the…

The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…

Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large…