Related papers: Conditional Effects, Observables and Instruments
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…
For a projective measurement, the Born rule provides the probability for an outcome in terms of the inner product between a projector and a quantum state. If the projector represents a pure entangled state and the state for a composite…
The purpose of this paper is to present a mathematical theory that can be used as a foundation for statistics that include improper priors. This theory includes improper laws in the initial axioms and has in particular Bayes theorem as a…
We study conditioning on null events, or surprises, and behaviorally characterize the Ordered Surprises (OS) representation of beliefs. For feasible events, our Decision Maker (DM) is Bayesian. For null events, our DM considers a hierarchy…
The von Neumann interaction between a particle and an apparatus has been considered in the measurement of the position of a particle when the interaction lasts for a finite amount of time. When the measurement has finite duration, both the…
Many observers can simultaneously measure different parts of an environment of a quantum system in order to find out its state. To study this problem we generalize the formalism of conditional master equations to the multiple observer case.…
The role of time in quantum mechanics is discussed. The differences between ordinary observables and an observable which corresponds to the time of an event is examined. In particular, the time-of-arrival of a particle to a fixed location…
We propose a class of incompatibility measures for quantum observables based on quantifying the effect of a measurement of one observable on the statistics of the outcomes of another. Specifically, for a pair of observables $A$ and $B$ with…
Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption,…
Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…
In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed even if we have perfect initial knowledge. That is, if the system is quantum the conditional…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
A class of k-particle observables in a two-mode system of Bose particles is characterized by typicality: if the state of the system is sampled out of a suitable ensemble, an experimental measurement of that observable yields (almost) always…
The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting…
We distinguish two questions (i) how much information does the prior contain? and (ii) what is the effect of the prior? Several measures have been proposed for quantifying effective prior sample size, for example Clarke [1996] and Morita et…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the typical…
It is well-known that a quantum measurement can enhance the transition probability between two quantum states. Such a measurement operates after preparation of the initial state and before postselecting for the final state. Here we analyze…
The problem of defining quantum probabilities of composite events is considered. This problem is of high importance for the theory of quantum measurements and for quantum decision theory that is a part of measurement theory. We show that…
In the context of generalized measurement theory, the Gleason-Busch theorem assures the unique form of the associated probability function. Recently, in Flatt et al. Phys. Rev. A 96, 062125 (2017), the case of subsequent measurements has…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…