**3. The quantum theory as usually presented in terms of Bayesian approach**

*"To suppose that, whenever we use a singular substantive [e.g. "information], we are, or ought to be, using it to refer to something, is an ancient, but no longer a respectable, error." [8],*

Taking Strawson's stricture of construing 'information' as a singular substantive, disembodied abstract entity as "an ancient, but no longer a respectable error," we need to look at **the probability approach** as a possible alternative.

The fallacy of construing information as a disembodied abstract entity can be avoided by taking *information as a range of possible results with varying probabilities*. Abstractly, information can be thought of as the resolution of uncertainty. While probability theory allows us to make uncertain statements and reason in the presence of uncertainty, information allows us to quantify the amount of uncertainty in a probability distribution, Let take an example, suppose we wish to compute the probability whether a poker player will win a game provided she possesses certain set of cards, exactly the same probability formulas would be used in order to compute the probability that a patient has a specific disease when we observe that she has certain symptoms. The reason for this is as follows: Probability theory provides as a set of formal rules for determining the likelihood of a proposition being true given the likelihood of other propositions.

It was in the second half of the 18th century, there was no branch of mathematical sciences called "Probability Theory". It was known simply by a rather odd-sounding "*Doctrine of Chances*". An article called, "*An Essay towards solving a Problem in the Doctrine of Chances*", authored by Thomas Bayes [9], was read to Royal Society and published in the *Philosophical Transactions of the Royal Society of London,* in 1763.

In this essay, Bayes described a simple theorem concerning joint probability which gives rise to the calculation of inverse probability. This is called Bayes' Theorem. It shows that there is a link between *Bayesian inference* and *information theory* that is useful for model selection, assessment of information entropy and experimental design.

$$\begin{array}{cc} \text{Posterior probability} \\ p(A|B) \end{array} = \frac{\text{Likelihood Price probability}}{p(B|A)} \qquad \text{(A)} \tag{1}$$

What is conveyed by this formula is that we update our belief, (i.e. *prior probability*), after observing the data/evidence (or the *likelihood*) of the belief and assign the updated degree of belief the term *posterior probability*. Our starting point could be a belief, however each data point will either strengthen or weaken that belief and this is how we update our belief or hypothesis all the time.

#### **3.1 Objective certainty in finite probability spaces**

In 1935, Einstein, Podolsky, and Rosen made the following sufficient condition for reality. Einstein, Podolsky and Rosen maintain that

*"If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity. [In this sense], can quantum-mechanical description of physical reality be considered complete?" [10],*

Rudolf Carnap and Yehoshua Bar-Hillel, also in Carnap Rudolf and Bar-Hillel Yehoshua [11] *'An Outline of a Theory of Semantic Information'*, take a probabilistic approach that capitalizes on the notion of the uncertainty of a piece of information in a given probability space.

#### **3.2 The essential claim of quantum Bayesian approach**

Quantum theory (as usually presented with the Born Rule, in its simplest form), states that the probability density of finding a particle at a given point, when measured, is proportional to the square of the magnitude of the particle's wave function at that point. It provides an algorithm for generating probabilities for alternative outcomes of a measurement of one or more observables on a quantum system. Traditionally they are regarded as objective. On the other hand, a subjective Bayesian or personalist view of quantum probabilities regard quantum state assignments as subjective.

#### **3.3 Critical remarks**

At the turn of the 21st century Quantum Bayesianism emerged as a result of the collaborative work among Caves et al. [12].

First, the word "Bayesian" does not carry a commitment to denying objective probability and a "Quantum Bayesian" insists that probability has no physical existence even in a quantum world. The probability ascriptions arise from a particular state that are understood in a purely Bayesian manner. Caves, Fuchs, and Schack refute Einstein, Podolsky, and Rosen's argument that quantum description is incomplete by giving up all objective physical probabilities. They would rather identify probability 1 with an **agent's subjective certainty**.

Secondly, the quantum state ascribed to an individual system is understood to represent a compact summary of **an agent's degrees of belief** about what the results of measurement interventions on a system are. Thus, an agent's degree of belief in terms of Quantum Bayesian approach is quite **subjective** and hence it would be characterized by a **non-realist view** of the quantum state.
