Related papers: A refinement of quantum mechanics by algorithmic r…
Quantum theory has evolved from a set of provisional rules to an indispensable framework that underlies much of modern technology and infrastructure. Yet, after a century, Born's probability postulate remains at odds with the theory's…
The subjective Bayesian interpretation of probability asserts that the rules of the probability calculus follow from the normative principle of Dutch-book coherence: A decision-making agent should not assign probabilities such that a series…
QBism regards quantum mechanics as an addition to probability theory. The addition provides an extra normative rule for decision-making agents concerned with gambling across experimental contexts, somewhat in analogy to the double-slit…
Probabilities in quantum theory are traditionally given by Born's rule as the expectation values of projection operators. Here it is shown that Born's rule is insufficient in universes so large that they contain identical multiple copies of…
We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is…
The Born rule is derived from operational assumptions, independent of the normalization of the state. Unlike Gleason's theorem, the argument applies even if probabilities are defined for only a single resolution of the identity, so it…
The Born rule, a foundational axiom used to deduce probabilities of events from wavefunctions, is indispensable in the everyday practice of quantum physics. It is also key in the quest to reconcile the ostensibly inconsistent laws of the…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
The Born postulate can be reduced to its deterministic content that only applies to eigenvectors of observables: the standard probabilistic interpretation of generic states then follows from algebraic properties of repeated measurements and…
The Born rule postulates that the probability of measurement in quantum mechanics is related to the squared modulus of the wave function $\psi$. We rearrange the equation for energy eigenfunctions to define the energy as the real part of…
QBism is one of the main candidates for an epistemic interpretation of quantum mechanics. According to QBism, the quantum state or the wavefunction represents the subjective degrees of belief of the agent assigning the state. But, although…
In Everettian quantum mechanics, justifications for the Born rule appeal to self-locating uncertainty or decision theory. Such justifications have focused exclusively on a pure-state Everettian multiverse, represented by a wave function.…
While the Born rule is traditionally introduced as a separate postulate of quantum mechanics, we show it emerges naturally from a modified Schr\"odinger equation that includes "small-signal truncation". This parallels the way quantum…
The paper discuss the structure of quantum mechanics and uniqueness of its postulates. The Born rule for quantum probabilities is fixed by requirement of nonexistence of quantum telepathy. Von Neumann projection postulate describes the…
In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a natural transformation of functors. In…
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
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…
Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in…
In quantum operations, probabilities characterise both the degree of the success of a state transformation and, as density operator eigenvalues, the degree of mixedness of the final state. We give a unified treatment of pure-to-pure state…
The notion of state vector is, in quantum mechanics, as central as it is problematic, as illustrates the wealth of publications about the sub- jects, including in particular the many attempts to obtain an acceptable interpretation of…