Related papers: Randomness from causally independent processes
Quantum causality extends the conventional notion of fixed causal structure by allowing channels and operations to act in an indefinite causal order. The importance of such an indefinite causal order ranges from the foundational---e.g.…
If quantum mechanics is taken for granted the randomness derived from it may be vacuous or even delusional, yet sufficient for many practical purposes. "Random" quantum events are intimately related to the emergence of both space-time as…
Random numbers are used in a wide range of sciences. In many applications, generating unpredictable private random numbers is indispensable. Device-independent quantum random number generation is a framework that makes use of the intrinsic…
Quantum theory allows the traversing of multiple channels in a superposition of different orders. When the order in which the channels are traversed is controlled by an auxiliary quantum system, various unknown parameters of the channels…
A scenario is outlined for quantum measurement, assuming that self-sustaining classicality is the consequence of an attractive gravitational self-interaction acting on massive bodies, and randomness arises already in the classical domain. A…
The standard method to check for the independence of two real-valued random variables -- demonstrating that the bivariate joint distribution factors into the product of its marginals -- is both necessary and sufficient. Here we present a…
Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions --…
Randomness is a valuable resource in science, cryptography, engineering, and information technology. Quantum-mechanical sources of randomness are attractive because of the indeterminism of individual quantum processes. Here we consider the…
Quantum processes can exhibit scenarios beyond a fixed order of events. We propose information inequalities that, when violated, constitute sufficient conditions to certify quantum processes without a fixed causal order -- causally…
Quantum mechanics allows for situations where the relative order between two processes is entangled with a quantum degree of freedom. Here we show that such entanglement can enhance the ability to transmit quantum information over noisy…
In classical physics, events follow a definite causal order: the past influences the future, but not the reverse. Quantum theory, however, permits superpositions of causal orders -- so-called indefinite causal orders -- which can provide…
We consider the problem of generating correlated random variables in a distributed fashion, where communication is constrained to a cascade network. The first node in the cascade observes an i.i.d. sequence $X^n$ locally before initiating…
This work is motivated by a question at the heart of unsupervised learning approaches: Assume we are collecting a number K of (subjective) opinions about some event E from K different agents. Can we infer E from them? Prima facie this seems…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…
We introduce an information-theoretic method for quantifying causality in chaotic systems. The approach, referred to as IT-causality, quantifies causality by measuring the information gained about future events conditioned on the knowledge…
For binary experimental data, we discuss randomization-based inferential procedures that do not need to invoke any modeling assumptions. We also introduce methods for likelihood and Bayesian inference based solely on the physical…
Quantum random number generation (QRNG) is a resource that is a necessity in the field of cryptography. However, its certification has been challenging. In this article, we certify randomness with the aid of quantum entanglement in a device…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…