Related papers: Conditional expectations associated with quantum s…
We consider the problem of constructing a "universal set" of Markovian processes, such that any Markovian open quantum system, described by a one-parameter semigroup of quantum channels, can be simulated through sequential simulations of…
To make sense of the world around us, we develop models, constructed to enable us to replicate, describe, and explain the behaviours we see. Focusing on the broad case of sequences of correlated random variables, i.e., classical stochastic…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a stochastic process with uncertain parameters. We develop a general framework which can be seen as a version of the martingale problem method…
In this article we propose a qualitative (ordinal) counterpart for the Partially Observable Markov Decision Processes model (POMDP) in which the uncertainty, as well as the preferences of the agent, are modeled by possibility distributions.…
We present a general theory of quantum information processing devices, that can be applied to human decision makers, to atomic multimode registers, or to molecular high-spin registers. Our quantum decision theory is a generalization of the…
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form a time series. Individual time series are realizations of a stochastic process over the…
We present a comparative study between classical probability and quantum probability from the Bayesian viewpoint, where probability is construed as our rational degree of belief on whether a given statement is true. From this viewpoint,…
Modeling and reasoning about concurrent quantum systems is very important both for distributed quantum computing and for quantum protocol verification. As a consequence, a general framework describing formally the communication and…
In ordinary Quantum Mechanics only ideally instantaneous observations of a quantity or a set of compatible quantities are usually considered. In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of…
The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is…
We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
Assuming the validity of the equivalence principle in the quantum regime, we argue that one of the assumptions of the usual definition of quantum mechanics, namely separation between the ``classical'' detector and the ``quantum'' system,…
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
Recent developments in quantum computing suggest that it could be possible to make conditional changes to the state of a quantum mechanical system without resorting to classical observation. It is accomplished through collective response of…
The disjunction effect in human decision making is often taken to show that the classical law of total probability is violated, motivating quantum-like models. We re-examine this claim for the Prisoner's Dilemma disjunction effect. Under…
Quantum mechanics, in principle, allows for processes with indefinite causal order. However, most of these causal anomalies have not yet been detected experimentally. We show that every such process can be simulated experimentally by means…