Theory

What is a bit? Where did the notion of a bit come from? To understand such essential concepts one should truly understand Shannon's Information Theory. What is to be understood, is that a bit is nothing but a measure of information. Weight (mass?) is measured in kilograms, length in metres, and information (data?) in bits. The minimum amount of information that can exist is a bit. A bit contains information about a certain flag, as to in which of these states it lies: TRUE (1, high, on) or FALSE (0,low, off). How is this information sufficient enough to do anything with it? Because we already know what that flag was intended for. We only needed to store the current state of the flag, and hence the bit.

Notice, that a flag can exist in only one of two states, T or F. Nothing intermediary. This is the basis of Binary Logic, Binary arithmetic and etc.. Arithmetic to the base 2. Why do we use only base 2 arithmetic? If we could store states 0, 1, 2, ... 9 in a "dit" (a decimal bit), we would obviously need a lot less number of dits to store the same information than the number of bits. So why is the number 2 sacred? Why does every computer use Binary logic instead of Decimal logic? The answer to that lies in material sciences. We have transistors that can work in between two electrical levels. Each of these electrical levels (, , VDD/VCC, etc.. ) can represent only one state, so there can be only two states represented by the transistor. And besides, arithmetic that can be done with any base can also be done with base 2. In other words, Decimal logic, is no more powerful (in terms of calculational possibilities) than Binary Logic. Hence the whole idea of Flip-Flops, etc.

Why am i talking about bits and pieces? What is the whole picture here? Basically i wanted to talk about "Qubits". Quantum Theoretic equivalents, of the Information theoretic bit. When we said any dits or other-its are as powerful as bits, why are we talking about these qubits? coz they come under a wholly different category. A qubit can exist in infinitely many states!

eh? what does that mean?

Think of an electron. It has spin angular momentum, according to our highschool physics text books, of either or . Let us represent the spin with say 0 and spin with 1. These states are mutually exclusive, in that no electron can exist in both these states at once. But what is interesting, and what is not taught in high school text books, is that an electron can exist in a combination of these two states! But hey! Didn't we learn that spin angular momentum of an electron was only either ? Now what's this about combination of states? Ahha. There in, lies the secret of the principle of Superposition.

What is not apparent at the first glance, is that outcomes of an experiment may not indeed tell you everything about the state of the system before the experiment. What I'm trying to say, is that we (meaning most computer scientists and almost all engineers) are so used to the black box approach, that we assume we know everything about a system and the states it might have been in, once we know the inputs and outputs through that black box. Maybe, this is not true in the Quantum world. Or is it? I really don't know. What I do know, is that we can never really say that an electron was in such a place in such a time (remember? Heisenberg's uncertainty principle?). When you can't even say that, or the direction in which it is spinning, how can we say whether it had a positive or a negative spin angular momentum? What in fact happens, or is theorized to happen, is that electrons might be spinning in a mixed state. Meaning they have a little of and a little of spin. But the moment we try to measure which of these it has, the state "collapses" to either one of them. Imagine a vector , which is neither completely a real number, nor completely a non-real number. But the moment you take a projection of this vector along one of the axes, the vector "collapses" to its component along that axis. This is how I understood what happens, when an experiment is done. The state of the system collapses to the observed state. But there is a difference to be noted, which might be the difference between a classical system and a quantum system. In the case of the vector, we knew a priori the axis that we were going to project the vector upon. This is not the case with a quantum experiment. You do indeed observe either a or a spin only for an electron, but you can never tell which value the result of the experiment will be. So essentially, an electron before measuring its spin angular momentum is in a state that is neither of the observable states, but in fact, a mixture of both and a lot more. Which is what I mean when I say a qubit exists in infinitely many states!


Now having said all of this, I still am not really sure whether what I've written is anywhere even remotely near to the physical/mathematical/scientific reality that I proclaim to study! (What is it that I proclaim to study? Please... )