Introduction to quantum bits and the polarization experiment!

Hi there! Quantum computing is a field buzzing with incredible potential, and at its heart lies: the quantum bit, or qubit. Think of qubits as the fundamental building blocks of quantum information, much like the 0s and 1s are for our everyday computers.
While classical bits can be represented in countless ways (like a light switch being on or off), qubits also manifest in diverse physical systems. But what truly matters in the quantum world isn't how they're built, but how they behave. And that's where things get really interesting!

The Polarization Experiment
To truly grasp the essence of qubits, let's dive into a fascinating real-world example: polarized photons. Imagine these as tiny particles of light, each with a specific orientation. This orientation can be precisely controlled and measured, making them perfect candidates for physically realizing a qubit.
Ready for the experiment? You can even try it at home (with proper safety precautions, of course!)
What you'll need:

• A laser pointer (your light source)

• Three polaroid filters (these only let light through in a specific direction)

Let's begin!
Single Polaroid (A): Shine your laser through polaroid A, oriented horizontally. You'll notice the light intensity drops by half. This is because the polaroid acts like a gate, only allowing light polarized in its direction to pass through.
Two Orthogonal Polaroids (A and C): Now, place polaroid C after A, but rotate C so it's vertical (90 degrees to A). What happens? No light gets through! The two polaroids are like an impenetrable wall, blocking all photons because their preferred directions are perpendicular.
The Quantum Twist: Three Polaroids (A, B, and C): Here's where the magic truly unfolds. Insert polaroid B between A and C, and set B at a 45-degree angle. Surprisingly, some light now reaches the screen! The light is brightest when B is exactly at 45 degrees.
Mind-blown, right? If two polaroids block all the light, how can adding a third one let some through? It's a fundamental characteristic of quantum systems.

The Quantum Unveiling: Why This Happens
While a strong light beam can be explained with classical wave physics, the real revelation comes when you use extremely dim light, so faint that only one photon passes at a time. In this scenario, classical explanations fails. Only quantum mechanics can make sense of it!
The Quantum Model of Polarization:
In the quantum world, a photon's polarization isn't just a simple direction; it's described as a unit vector (a mathematical "arrow" of length 1). We use special notations to represent these states:

• $|\uparrow ⟩$ for vertical polarization

• $|\to ⟩$ for horizontal polarization

The truly astonishing part is that any polarization can be described as a superposition of these two basic directions:

Here, 'a' and 'b' are numbers called amplitudes, telling us how much of each direction is present. For instance, a photon polarized at 45 degrees looks like this:

So, what's truly happening to our photons? When a photon passes through the first horizontal polaroid, it becomes horizontally polarized. But when it encounters the 45-degree polaroid, it doesn't just stay horizontal. Instead, it enters a superposition – a dynamic mix of both horizontal and vertical polarization!

Measurement and Probability
When a photon hits a polaroid, the polaroid acts like a "measuring device" with a preferred axis (its orientation).

• The polaroid has a "preferred axis" (its orientation).
• The probability the photon gets through is the square of the amplitude in the polaroid's direction.
• If it gets through, it's polarization matches the polaroid's axis.
• If not, it's absorbed.

This is why the third polaroid matters! After passing through horizontal polaroid A, the photon is purely horizontal ($|\to ⟩$). If it then hits vertical polaroid C, it's blocked. But by inserting the 45-degree polaroid B, the photon can become polarized at 45 degrees. Since a 45-degree photon has a non-zero vertical component, some of these photons can then pass through the final vertical polaroid C!

Key Quantum Principles in Action
This seemingly simple experiment beautifully illustrates core principles of quantum mechanics that are fundamental to qubits:

• Superposition: A qubit can exist in a "mix" of multiple states simultaneously (like being both horizontal and vertical at the same time!), not just a definite 0 or 1.

• Measurement: When you measure a qubit, you get a definite outcome, but this outcome is probabilistic, determined by the amplitudes of its superposition.

• State Change: The act of measurement fundamentally changes the qubit's state to match the result of that measurement.

Dirac's Bra/Ket Notation

You might have noticed the fancy notation like ∣v⟩. This is Dirac's Bra/Ket Notation, and it's the standard way to write quantum states (called "kets") in quantum mechanics and quantum computing. It's a concise and powerful way to describe the complex quantum world!

This is just the beginning of understanding qubits and the immense possibilities they unlock for the future of computing!