Hands-On Introduction to Quantum Entanglement

There’s a lot of buzz around quantum computing. Some emphasize the notion of the qubit being in the two states concurrently, and that’s different from anything we know. In the world we live in, and the world we experience, there’s nothing that exists in two mutually exclusive states, simultaneously.

Others argue that this notion is wrong. The qubit is not 0 and 1 at the same time, but a truly random system. But in the world that we perceive, everything is dependent on initial conditions. If we were able to measure everything with absolute precision, randomness would disappear.

There are counters to this notion as well, but the whole concept of quantum superposition is so different from anything we know, and there’s nothing in our present world that is comparable. Any analogy, thereby, would be inadequate.

So far, the only aspect of the quantum superposition we’ve covered is the probability of measuring it as either 0 or 1. Yes, it is interesting. It may even seem a little strange. But a system whose value depends on chance is not unimaginable. From what we’ve seen so far, it’s a probabilistic system and it doesn’t matter if the qubit is in both states concurrently, purely random, or something completely different. We’ve only considered a single qubit so far, so let’s take a look at how things change if we were to work with multiple qubits.

We already know some operations that work with multiple classical bits, such as and and or. A look at the truth tables discloses that they are inappropriate for qubit transformation. They are irreversible.

While there are two input values ($P$ and $Q$), either and or or on its own will have only one output value. It’s impossible to reconstruct the two input bits if we only got one output bit as information. So, when we work with two qubits, any operator (the transformation gate) must have two outputs.

Can we use and and or as the two outputs?

No, we can’t. These two operations don’t allow us to tell the difference between the states in which either one of $P$ and $Q$ ...