Related papers: From time-reversal symmetry to quantum Bayes' rule…
A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over…
The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global…
We introduce the notion of time reversal in open quantum systems as represented by linear quantum operations, and a related generalization of classical entropy production in the environment. This functional is the ratio of the probability…
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,…
We give a consistent quantum description of time, based on Page and Wootters' conditional probabilities mechanism, that overcomes the criticisms that were raised against similar previous proposals. In particular we show how the model allows…
This paper reports three almost trivial theorems that nevertheless appear to have significant import for quantum foundations studies. 1) A Gleason-like derivation of the quantum probability law, but based on the positive operator-valued…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
The Born rule, which is one of foundational axioms of quantum theory, states that the probability of obtain outcome $a$ for the quantum state $|\psi\rangle$ is determined by $P(a)=|\langle a|\psi\rangle|^{2}$. Despite its great success in…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
I show that probabilities in quantum mechanics are a measure of belief in the presence of human ignorance, just like all other probabilities. The Born interpretation of the square of modulus of the wave function arises from the interaction…
We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference,…
The principle of teleportation can be used to perform a quantum computation even before its quantum input is defined. The basic idea is to perform the quantum computation at some earlier time with qubits which are part of an entangled…
A new formulation of quantum mechanics is developed which does not require the concept of the wave-particle duality. Rather than assigning probabilities to outcomes, probabilities are instead assigned to entire fine-grained histories. The…
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…
Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other…
There exists a stark tension among different formulations of quantum theory as some are inherently time-symmetric while others are time-asymmetric. This tension is crisply captured when considering physical theories as theories of…