Wednesday, December 4, 2024

Quantum Communications - Part 3: Photon Polarization and Superposition

 Building on Part 2’s discussion of polarization, let's look a little deeper at how light enables quantum communication. Superposition in quantum mechanics means a photon can exist in multiple polarization states at once, unlike classical objects that must be in one definite state. Looking at the diagram below, a photon isn't limited to being just vertical (1) or horizontal (0), but can exist in a mixture of both until measured. Think of it like a spinning coin - while spinning, it's neither heads nor tails but both possibilities at once. When we measure the photon's polarization (like catching the coin), it "collapses" into one definite state.

The diagram shows two measurement bases - rectilinear and diagonal. A photon in superposition measured in either base has a probability of being found in either state of that base. This property is crucial for quantum cryptography because any measurement by an eavesdropper forces the superposition to collapse, altering the photon's state and revealing the intrusion.

 

The 45° polarization state, shown in the diagonal base of our diagram, demonstrates one of the most fascinating aspects of quantum mechanics. While we might classically think of 45° as simply an angle halfway between horizontal and vertical, in quantum mechanics it represents something far more profound. When a photon is polarized at 45°, it literally exists in a perfect blend of horizontal and vertical states at the same time - not just leaning one way or the other, but fully in both states simultaneously.

 

This quantum behavior becomes clear when we measure these 45° polarized photons. If we measure using the rectilinear base (horizontal/vertical as shown in the left circle of our diagram), we get the following result: the photon will randomly show up as either horizontal or vertical with exactly equal probability. This isn't because we're measuring imprecisely or because the photon was "kind of" in both states - it was genuinely, mathematically, and physically in both states at once until the act of measurement forced it to pick one.

 

Think of it this way: if we send many 45° polarized photons through a horizontal polarizer, exactly half will pass through (registering as horizontal) and half will be blocked (registering as vertical). This isn't due to some classical "angled" behavior - it's a direct manifestation of quantum superposition, where the photon existed in both states simultaneously until we forced it to "decide" by measuring it.

 

This property is part of what makes quantum communication so secure: any attempt to measure these superposition states unavoidably disturbs them, making eavesdropping detectable.