Related papers: Operational restrictions in general probabilistic …
In a Generalised Probabilistic Theory (GPT) equipped additionally with some extra geometric structure we define the morphophoric measurements as those for which the measurement map sending states to distributions of the measurement results…
Limitation of computational resources is considered as a universal principle that for simulation is as fundamental as physical laws are. It claims that all experimentally verifiable implications of physical laws can be simulated by the…
Similar formalisms have been independently developed in psychology, to deal with the issue of selective influences (deciding which of several experimental manipulations selectively influences each of several, generally non-independent,…
Given a set of probability measures $\mathcal{P}$ representing an agent's knowledge on the elements of a sigma-algebra $\mathcal{F}$, we can compute upper and lower bounds for the probability of any event $A\in\mathcal{F}$ of interest. A…
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.…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
Resource theories provide a general framework for the characterization of properties of physical systems in quantum mechanics and beyond. Here, we introduce methods for the quantification of resources in general probabilistic theories…
Projection factors describe the contraction of Lebesgue measures in orthogonal projections between subspaces of a real or complex inner product space. They are connected to Grassmann's exterior algebra and the Grassmann angle between…
Quantum theory combines density matrices, Born probabilities, tensor-product composites, positive-operator-valued measures (POVMs), and quantum channels. In a finite-dimensional causal operational theory, we prove that two postulates…
The structure of a local hidden variable model for experiments involving sequences of measurements rigorously is analyzed. Constraints imposed by local realism on the conditional probabilities of the outcomes of such measurement schemes are…
We introduce multi-object operational tasks for measurement incompatibility in the form of multi-object quantum subchannel discrimination and exclusion games with prior information, where a player can simultaneously harness the resources…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
Complex metrics are a double-edged sword: they allow one to replace singular spacetimes, such as those containing a big bang, with regular metrics, yet they can also describe unphysical solutions in which quantum transitions may be more…
Generalised observables (POM observables) are necessary for representing all possible measurements on a quantum system. Useful algebraic operations such as addition and multiplication are defined for these observables, recovering many…
Negative probabilities have long been discussed in connection with the foundations of quantum mechanics. We have recently shown that, if signed measures are allowed on the hidden variables, the class of probability models which can be…
The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…
Standard projective measurements represent a subset of all possible measurements in quantum physics, defined by positive-operator-valued measures. We study what quantum measurements are projective simulable, that is, can be simulated by…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…