Related papers: Is Bayes theorem applicable to all quantum states?
It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is…
This paper is devoted to clarification of the notion of entanglement through decoupling it from the tensor product structure and treating as a constraint posed by probabilistic dependence of quantum observable A and B. In our framework, it…
Can quantum theory be applied on all scales? While there are many arguments for the universality of quantum theory, this question remains a subject of debate. It is unknown how far the existence of macroscopic irreversibility can be derived…
In simple -- but selected -- quantum systems, the probability distribution determined by the ground state wave function is infinitely divisible. Like all simple quantum systems, the Euclidean temporal extension leads to a system that…
Entanglement and nonlocality are both fundamental aspects of quantum theory, and play a prominent role in quantum information science. The exact relation between entanglement and nonlocality is however still poorly understood. Here we make…
Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds…
It is usually assumed that the quantum state is sufficient for deducing all probabilities for a system. This may be true when there is a single observer, but it is not true in a universe large enough that there are many copies of an…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
We review the Consistent Amplitude approach to Quantum Theory and argue that quantum probabilities are explicitly Bayesian. In this approach amplitudes are tools for inference. They codify objective information about how complicated…
We argue that quantum gravity should be a super-quantum theory, that is, a theory whose non-local correlations are stronger than those of canonical quantum theory. As a super-quantum theory, quantum gravity should display distinct…
We attempt a justification of a generalisation of the consistent histories programme using a notion of probability that is valid for all complete sets of history propositions. This consists of introducing Cox's axioms of probability theory…
A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple…
In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…
It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such…
Two or more quantum systems are said to be in an entangled or non-factorisable state if their joint (supposedly pure) wave-function is not expressible as a product of individual wave functions but is instead a superposition of product…
Does the notion of a quantum randomized or nondeterministic algorithm make sense, and if so, does quantum randomness or nondeterminism add power? Although reasonable quantum random sources do not add computational power, the discussion of…
The implications of the physical theory of quantum mechanics on the question of realism is much a subject of sustaining interest, while the background questions among physicists on how to think about all the theoretical notion and…
Bayes factors are characterized by both the powerful mathematical framework of Bayesian statistics and the useful interpretation as evidence quantification. Former requires a parameter distribution that changes by seeing the data, latter…
We investigate operational probabilistic theories where the pure states of every system are the vertices of a simplex. A special case of such theories is that of classical theories, i.e. simplicial theories whose pure states are jointly…
It is argued that there is no evidence for causality as a metaphysical relation in quantum phenomena. The assumption that there are no causal laws, but only probabilities for physical processes constrained by symmetries, leads naturally to…