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We show that three fundamental information-theoretic constraints--the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the…
Signal causality, the prohibition of superluminal information transmission, is the fundamental property shared by quantum measurement theory and relativity, and it is the key to understanding the connection between nonlocal measurement…
Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities.…
It is often supposed that a quantum system is not disturbed without state change. In a recent debate, this assumption is used to claim that the operator-based disturbance measure, a broadly used disturbance measure, has an unphysical…
We show that the formulations of non-relativistic quantum mechanics can be derived from an extended least action principle. The principle extends the least action principle from classical mechanics by factoring in two assumptions. First,…
Correlation self-testing of quantum theory involves identifying a task or set of tasks whose optimal performance can be achieved only by theories that can realise the same set of correlations as quantum theory in every causal structure.…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
Spekkens has introduced an epistemically restricted classical theory of discrete systems, based on discrete phase space. The theory manifests a number of quantum-like properties but cannot fully imitate quantum theory because it is…
In this article, we continue our investigation on the role of non-commutativity in quantum theory. Using the method explained in "On non-commutativity in quantum theory (I): from classical to quantum probability", we analyze two toy models…
Quantum information cannot be broadcast -- an intrinsic limitation imposed by quantum mechanics. However, recent advances in virtual operations offer new insights into the no-broadcasting theorem. Here, we focus on the practical utility and…
An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations…
We investigate the quantum theory of closed systems based on the linear positivity decoherence condition of Goldstein and Page. A quantum theory of closed systems requires two elements; 1) a condition specifying which sets of histories may…
Finding physical principles lying behind quantum mechanics is essential to understand various quantum features, e.g., the quantum correlations, in a theory-independent manner. Here we propose such a principle, namely, no disturbance without…
Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order…
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
The Pusey-Barrett-Rudolph (PBR) no-go theorem provides an argument for the reality of the quantum state by ruling out {\psi}-epistemic ontological theories, in which the quantum state is of a statistical nature. It applies under an…
The no-broadcasting theorem is a fundamental result in quantum information theory. It guarantees that a class of attacks on quantum protocols, based on eavesdropping and indiscriminate copying of quantum information, are impossible. Due to…
The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it…
We derive the quantum stochastic master equation for bosonic systems without measurement theory but control theory. It is shown that the quantum effect of the measurement can be represented as the correlation between dynamical and…
In this paper, we build double theories capturing the idea of nondeterministic behaviors and trajectories. Following Libkind and Myers' Double Operadic Theory of Systems, we construct monoidal semi double categories of interfaces, along…