Related papers: Generating Randomness from a Computable, Non-rando…
Quantum statistics originate from the physics of state preparation. It is therefore wrong to think of quantum states as fundamental. In fact, quantum states are merely summaries of dynamical processes that randomize the properties of the…
Random number has many applications, it plays an important role in quantum information processing. It's not difficult to generate true random numbers, the main difficulty is how to certify the random numbers generated by untrusted devices.…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
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…
This paper explores a novel definition of Schnorr randomness for noncomputable measures. We say $x$ is uniformly Schnorr $\mu$-random if $t(\mu,x)<\infty$ for all lower semicomputable functions $t(\mu,x)$ such that $\mu\mapsto\int…
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…
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a…
A semi-measure is a generalization of a probability measure obtained by relaxing the additivity requirement to super-additivity. We introduce and study several randomness notions for left-c.e. semi-measures, a natural class of effectively…
We investigate how much randomness can be extracted from a generic partially entangled pure state of two qubits in a device-independent setting, where a Bell test is used to certify the correct functioning of the apparatus. For any such…
We study randomness beyond $\Pi^1_1$-randomness and its Martin-L\"of type variant, introduced in \cite{MR2340241} and further studied in \cite{Continuous-higher-randomness}. The class given by the infinite time Turing machines (\ITTM s),…
Algorithmic randomness theory starts with a notion of an individual random object. To be reasonable, this notion should have some natural properties; in particular, an object should be random with respect to image distribution if and only…
This paper is a comment on the paper "Quantum Mechanics and Algorithmic Randomness" was written by Ulvi Yurtsever \cite{Yurtsever} and the briefly explanation of the algorithmic randomness of quantum measurements results. There are…
The question of the generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. Particularly, we consider the generation of the random…
Random numbers represent an indispensable resource for many applications. A recent remarkable result is the realization that non-locality in quantum mechanics can be used to certify genuine randomness through Bell's theorem, producing…
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…
Intrinsic randomness is generated when a quantum state is measured in any basis in which it is not diagonal. In an adversarial scenario, we quantify this randomness by the probability that a correlated eavesdropper could correctly guess the…
Measurement-based quantum computation is a framework of quantum computation, where entanglement is used as a resource and local measurements on qubits are used to drive the computation. It originates from the one-way quantum computer of…
The numerical generation of random quantum states (RQS) is an important procedure for investigations in quantum information science. Here we review some methods that may be used for performing that task. We start by presenting a simple…
The distillable randomness of a bipartite quantum state is an information-theoretic quantity equal to the largest net rate at which shared randomness can be distilled from the state by means of local operations and classical communication.…