Related papers: Imprecise probability for non-commuting observable…
It is shown that the supersymmetric quantum mechanics has an octonionic generalization. The generalization is based on the inclusion of quaternions into octonions. The elements from the coset octonions/quaternions are unobservables bacause…
In classical probability theory, the best predictor of a future observation of a random variable $X,$ is its expected value $E_P[X]$ when no other information is available When information consisting in the observation of another random…
We propose two classes of nonparametric point estimators of $\theta=P(X<Y)$ in the case where $(X,Y)$ are paired, possibly dependent, absolutely continuous random variables. The proposed estimators are based on nonparametric estimators of…
Typical causal effects are defined based on the marginal distribution of potential outcomes. However, many real-world applications require causal estimands involving the joint distribution of potential outcomes to enable more nuanced…
The notion of incompressible momentum observables is introduced. It is shown that when the metric in a manifold has a certain form, a set of canonically conjugate variables Xk and Pk in which Pk are incompressible, can be constructed. Based…
In this letter, firstly, the Schr$\ddot{o}$dinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
Under a standard set of assumptions for a hidden-variables model for quantum events, we show that all observables must commute simultaneously. And, despite Bell's complaint that a key condition of von Neumann's was quite unrealistic, we…
We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system, which provides a state-independent maximum lower bound on the direct-sum of the probability vectors in terms of…
When estimating finite mixture models, it is common to make assumptions on the mixture components, such as parametric assumptions. In this work, we make no distributional assumptions on the mixture components and instead assume that…
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
The existence of incompatibility is one of the most fundamental features of quantum theory, and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A…
In this note, we consider the implications of the Heisenberg uncertainty principle (HUP) when computing uncertainties that affect the main dynamical quantities, from the perspective of special relativity. Using the well-known formula for…
The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
Quantum coherence is an exquisitely quantum phenomenon that depends on both probability amplitudes and relative phases. Standard coherence measures quantify superposition within density matrices but cannot distinguish ensembles that produce…
The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…
We show that including both the system and the apparatus in the quantum description of the measurement process, and using the concept of conditional probabilities, it is possible to deduce the statistical operator of the system after a…
It is shown that 'non-quantum systems', with anomalous statistical properties, would carry a distinctive experimental signature. Such systems can exist in deterministic hidden-variables theories (such as the pilot-wave theory of de Broglie…