Related papers: Is Bayes theorem applicable to all quantum states?
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum…
A collapse-free version of quantum theory is examined to systematically study the role of the projection postulate. This foil theory assumes "passive" measurements that do not update quantum states although measurement outcomes still occur…
In this paper, we show that Quantum Mechanics does not admit ontological models, in the sense that the quantum state of a system cannot correspond to a set of physical states representing the independent reality of the system. We show, via…
A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of…
Two basic properties of the set of all probability measures on the set of quantum states and their corollaries are considered. Several applications of these properties to analysis of functional constructions widely used in quantum…
In approaches to quantum theory in which the quantum state is regarded as a representation of knowledge, information, or belief, two agents can assign different states to the same quantum system. This raises two questions: when are such…
A well-known manifestation of quantum entanglement is that it may lead to correlations that are inexplicable within the framework of a locally causal theory --- a fact that is demonstrated by the quantum violation of Bell inequalities. The…
In ordinary situations involving a small part of the universe, Born's rule seems to work well for calculating probabilities of observations in quantum theory. However, there are a number of reasons for believing that it is not adequate for…
A fundamental question in quantum mechanics is, whether it is possible to replicate an arbitrary unknown quantum state. Then famous quantum no-cloning theorem [Nature 299, 802 (1982)] says no to the question. But it leaves open the…
Quantum theory is notoriously counterintuitive, and yet remains entirely self-consistent when applied universally. Here we uncover a new manifestation of its unusual consequences. We demonstrate, theoretically and experimentally (by means…
We address the problem of reconstructing quantum theory from the perspective of an agent who makes bets about the outcomes of possible experiments. We build a general Bayesian framework that can be used to organize the agent's beliefs and…
Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based…
The no-masking theorem for quantum information proves that it is impossible to encode an arbitrary input state into a larger bipartite entangled state such that the full information is stored in the correlation but the individual subsystems…
Zurek claims to have derived Born's rule noncircularly in the context of an ontological no-collapse interpretation of quantum states, without any "deus ex machina imposition of the symptoms of classicality." After a brief review of Zurek's…
It is shown that (i) all entangled states can be mapped by single-copy measurements into probability distributions containing secret correlations, and (ii) if a probability distribution obtained from a quantum state contains secret…
Despite various parallels between quantum states and ordinary information, quantum no-go-theorems have convinced many that there is no realistic framework that might underly quantum theory, no reality that quantum states can represent…
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As…
It is a fundamental prediction of quantum theory that states of physical systems are described by complex vectors or density operators on a Hilbert space. However, many experiments admit effective descriptions in terms of other state…
Probability theory can be modified in essentially one way while maintaining consistency with the basic Bayesian framework. This modification results in copies of standard probability theory for real, complex or quaternion probabilities.…
Bayesian implementation concerns decision making problems when agents have incomplete information. This paper proposes that the traditional sufficient conditions for Bayesian implementation shall be amended by virtue of a quantum Bayesian…