**4. 'Information is Physical' Approach: An alternative**

The fact that 'information is physical' means and that the laws of Quantum Mechanics can be used to process and transmit it in ways that are not possible with classical systems.

Thus, *Classical Information Theory* is the mathematical theory of information that involves processing tasks such as storage and transmission of information, whereas *Quantum Information Theory* is the study of how such tasks can be accomplished using quantum mechanical systems.

### **4.1 Foundational issues**

Quantum Physics, ever since it was advanced in the 1920s, has led to countless discussions about its meaning and about how to interpret the theory correctly. These discussions relate to the issues like the Einstein-Podolsky-Rosen paradox, quantum nonlocality and the role of measurement in quantum physics and several others. For example, in stating their paradox on the basis of a certain restricted set of correlations for a pair of systems in a particular entangled state (explained below), Einstein et al. [10], claimed that the phenomenon of entanglement conflicts with certain basic realist principles of separability and locality that all physical theories should respect. Otherwise we have to regard quantum states as'incomplete' descriptions of reality.

Challenging Einstein in 1927 during the **fifth Solvay Conference** (from October 24 to 29), on Electrons and Photons, which championed Quantum Theory, physicist Niels Bohr argued that the mere act of indirectly observing the atomic realm changes the outcome of quantum interactions. Nevertheless, according to Bohr, quantum predictions based on probability accurately describe reality. The so-called *Copenhagen interpretation*, which is a collection of views about the meaning of quantum mechanics principally attributed to Niels Bohr and Werner Heisenberg, also emerged in 1927. Bohr presented his view on quantum mechanics for the first time and Bohr's presentation of his view on quantum mechanics came to be called the Copenhagen interpretation, in honor of Bohr's home city. It combined his own idea of particle-wave complementarity with Max Born's probability waves and Heisenberg's uncertainty principle.

Earlier around 1926, Erwin Schrödinger had already developed a mathematical formula to describe such "matter waves", which he pictured as some kind of rippling sea of smeared-out particles. But Max Born showed that Schrödinger's waves are, in effect, "waves of probability". They encode the statistical likelihood that a particle will show up at a given place and time based on the behavior of many such particles in repeated experiments. When the particle is observed, something strange appears to happen: the wave-function "collapses" to a single point, allowing us to see the particle at a particular position.

In recent years research into the very foundations of quantum mechanics has given rise to the present field, i.e. Quantum Information Science and Technology. Thus the use of quantum physics could revolutionize the way we process and communicate information. The slogan that 'Information is Physical' is often presented as the fundamental insight at the heart of quantum information theory; after all 'information' is an abstract noun referring to something physical, transmitted from one point to another and it is frequently claimed to be entailed, or at least suggested, by the theoretical and practical advances of quantum information and computation.

#### **4.2 Claude Shannon**

The concept of information and technical notions of information, is derive from the work of Claude Shannon in his **A Mathematical Theory of Communication,**

Claude E. Shannon [1], Shannon's concept of information tells us the irreducible meaning content of the message, specified in bits, which somehow possess their own intrinsic meaning. However,

*"The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently these messages have meaning … These semantic aspects of communication are irrelevant to the engineering problem." ([1], p. 31)*

We must take note first that the notion of "information" in the semantic aspects of communication did not concern Shannon. His notion of "information" is often called **"mathematical information"** and it names a branch of study which deals with quantitative measures of information. For example, binary digit, or bit, can store two pieces of information, since it can represent two different states. Two bits can store four states, however: 00, 01, 10 and 11. Three bits can store eight states and so on. This can be generalized by the formula log2(x), where x represents the number of possible symbols in the system.

Secondly, Shannon, in his mathematical theory of information, introduces the term "**entropy**." Entropy is a key measure in information theory. It quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. We can illustrate it by identifying the outcome of a fair coin flip with two equally likely outcomes. It therefore provides less information or **lower entropy** than specifying the outcome from a roll of a die with six equally likely outcomes.

Shannon borrowed the term "entropy" from John von Neumann. However, in Shannon's undertaking, the notion of **'Information entropy'** tells us about **the measure of the uncertainty corresponding to unpredictability of a piece of information**. Thus, it is claimed that information that is highly probable, hence, more predictable, has a lower entropy value than less distributed information, since 'less distributed information' discloses less about the world.

Finally, the important aspect of communication can be specified by bits, which signify the physical aspect of the message and yet, somehow, it carries the meaning of the message from one point to another by encoding and decoding. However, in Shannon's mathematical theory of information, the messages in question will not have meaning. For example, while we talk in a telephone what is transmitted is not what is said into the telephone, but an analogue signal. This analogue signal records the sound waves made by the speaker, which is transmitted digitally following an encoding. Thus, a communication system consists of an information source, a transmitter or encoder, (possibly noisy) a channel, and a receiver or decoder. These are the physical aspect of the message and what mainly concerns information scientists and engineers.

John Barwise and Jerry Seligman [13], identify the 'inverse relationship principle'. The inverse relationship principle says that the informativeness of a piece of information increases as its probability decreases. This position is closely linked to the notion of *information entropy*. They claim that the quantification of semantic content demonstrates a firm relationship between semantic information and the mathematical quantification of data, previously envisioned by Shannon.

#### **4.3 Rolf Landauer**

Perhaps the most vociferous proponent of the idea that 'information is physical' was the late Rolf Landauer. In the two articles by him and one related to his work, viz., Landauer Rolf [14–17], Landauer made a very important and new observation, i.e. that information is not independent of the physical laws used to store and processes it. Information is physical, or is a fundamental constituent of the universe. Landauer's point is that whenever we find information, we find it inscribed or encoded somehow in a physical medium of whatever kind.

Although modern computers rely on quantum mechanics to operate, the information itself is still encoded classically.

*"Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe … information is inevitably inscribed in a physical medium" ([17], p. 63, 64).*

Moreover, it seems that Quantum Information Theory itself provides an apt illustration of the claim that 'Information is Physical'. But why is it that this claim is being made?

Since Landauer's very first work, viz., Landauer Rolf [14], "Dissipation and heat generation in the computing process," it was argued that information has a physical nature. As Galindo and Martin-Delgado in [18], point out that information is normally printed on a physical support, it cannot be transported faster than in vacuum, and it abides by natural laws. Moreover, they maintain that the statement that information is physical does not simply mean that a computer is a physical object, but in addition that information itself is a physical entity. In turn, this implies that the laws of information are restricted or governed by the laws of physics, in particular, those of quantum physics. Thus, information is not a disembodied abstract entity; it is always tied to a physical representation.

The first important results supporting the idea that "information is physical" was Landauer's **erasure principle**. it concerns the minimum amount of energy that has to be dissipated by a computing device when erasing one bit of information, The principle also states that the erasure of information is inevitably accompanied by the generation of heat. Bennett states the Principle in the following way: Landauer's **erasure principle** claims that

*"any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the informationprocessing apparatus or its environment" [19],*

It must be emphasized that Landauer's principle is valid both in classical and quantum physics.

Let us take a look at two ways the experts reacted to this view:

The question is: do the truly fundamental laws of nature concern, not waves and particles, but "information"?

According to one view the truly fundamental laws of Nature concern information, not waves or particles and it is taken to be the basic postulate. For example, it is known that quantum key distribution is possible but 'quantum bit' commitment is not and that nature is nonlocal (but not as nonlocal as is imposed by causality).

According to the other view: "Information is information, not matter or energy" ([20], p. 132).

This view will be supported by Shannon. For Shannon what a sender transmits to a receiver is not information but a message. While defining information Shannon is strictly concerned with the potential selections of messages or, more precisely, of the signs available in order to codify them, Shannon' theory does not come to grips with communication as transmission of meaning or with information as the meaning of a message. His theory is mainly concerned with codification and transmission of messages. It equates two terms that are apparently opposed, namely information and uncertainty. What Shannon aims to quantify is not an 'information flow,' [6], but the transmission of messages that can be continuous, discrete or mixed. This transmission is based on a medium or, more precisely, on a messenger and is understood as a formal relation between messages.
