# Quantum Entanglement

They say it takes two to tango and the same is true of quantum entanglement, a fundamental resource in our universe – like energy, whose properties we’ve only recently started to understand. Unlike quantum superposition, which is a property that can be exhibited by a single particle, entanglement requires the existence of two or more quantum subsystems; that is, it requires a decomposition of a quantum system into parts. As such, quantum entanglement is a property shared by parts of a larger whole, like the individual electrons (fundamental particles of electricity and magnetism) in a pair with zero total spin.

Let’s take a deep dive. In quantum mechanics, the state of such a pair is written as:

$\frac{1}{\sqrt{2}} |\uparrow>_1|\downarrow>_2 - \frac{1}{\sqrt{2}} |\downarrow>_1 |\uparrow>_2$

What you see above is a 50-50 quantum superposition. Let me break it down for you: The two numbers, $\frac{1}{\sqrt{2}}$ and $-\frac{1}{\sqrt{2}}$, are called the amplitudes. The two expressions $|\uparrow>_1|\downarrow>_2$ and $|\downarrow>_1 |\uparrow>_2$, represent the quantum states of the two electrons. Together, the amplitudes and the quantum states can give a complete description of everything in the universe. This is powerful stuff.

Now let’s dig a little further (in case you haven’t noticed, you are learning quantum mechanics right now). The amplitudes are usually fractions and they are associated with how often you would observe the particular quantum state in front of which they chill. The association of amplitudes with probabilities is simple: Take the (norm of the) amplitude and square it (e.g. 1/2 becomes 1/4, so you would observe that particular state about one-in-four times). And this is exactly why the quantum state I wrote above is a 50-50 superposition! The amplitudes square to 1/2, so each quantum state will be observed with 50% chance. We cannot know which state we will see (it is not for lack of trying – it is intrinsically a random choice of a multiverse branch), but half the time the pair of electrons will be in the state $|\uparrow>_1|\downarrow>_2$ and the other half they will be in the state $|\downarrow>_1 |\uparrow>_2$.

Now, here comes the weird part: The two electrons will always be observed to have opposite spin (when one has spin up, the other one will have spin down and vice versa). In other words, one electron wouldn’t know its own spin here on Earth, until the other electron passing near the Sun’s electromagnetic field decided to be spin up. Spooky action at a distance, indeed.

# Wrapping our brains around quantum mechanics

Quantum mechanics is not just difficult to learn, it literally doesn’t make sense. Our brains and language did not evolve to describe phenomena on that scale; classical intuition has no place In explaining superposition and entanglement.

The historical resolution of this incompatibility was to use the language of mathematics to model quantum mechanics. Over time, practitioners could develop a new kind of intuition based outside of their direct sensory experience.

qCraft represents a new kind of approach that was not available to Schrodinger. The partial differential equations used by working quantum mechanics reflect the information technology of the last century, a pencil and a piece of paper. Numerical simulation is essential in many areas of science, but it is not conventionally interactive and immersive in the way that Minecraft is. qCraft is not just a game, it’s a tool to extend our faculties.

Dr. Neil Gershenfeld is Director of the Center for Bits and Atoms at MIT.

# Quantum superposition

Without it, there can be no entanglement, no teleportation, no observational dependency. In fact, if time and space are emergent phenomena generated by the entanglement present in the wavefunction of the universe, then quantum superposition is responsible for the very existence of the concept of change – the illusion we have as local observers within the universe, that things evolve in time and move in space even if the total stays forever the same.

So, what exactly is quantum superposition?

Let’s start with an example of what it is not. Take a coin and flip it in the air. As it is rotating freely, the coin is neither heads, nor tails. It seems to be both at the same time, right? No, not really. And the reason is subtle. Imagine that instead of the coin spinning in the air, you attach the coin to a string hanging from the ceiling and then you start spinning (or, more appropriately, strafing) around the coin. The coin is spinning from your perspective, even though it is standing still. More importantly, the coin is always heads from one side and always tails from the opposite side – no matter how many times you spin around it. And therein lies the difference with quantum superposition: A quantum coin (which we call a qubit) will randomly flip between heads and tails, simply because you have the audacity to view it from “the side” as you are spinning. Indeed, if you close your eyes only to open them when you are facing the coin “head” on, then it will act like a regular coin.

So, next time someone asks you what quantum superposition is, don’t just say: Being two things at the same time! If that’s all there is to it, then my breakfast is quantum (oh wow, my breakfast is quantum!) since it is both nutritionally complete and super delicious. So, let’s rewind and focus on the quantum coin. What makes it quantum is the fact that there are two complementary (and incompatible) ways to look at it. If you look at it one way, the very fact that you looked makes the complementary outcome fundamentally random. Imagine how frustrating it would be to play on the quantum version of Let’s Make a Deal. Every time you open the wrong door, the big prize behind the other door has a 50-50 chance of disappearing! Not cool Monty Hall.

# qCraft 1.02 with Minecraft 1.6.4 support

We just released a minor update to qCraft (version 1.02). Version 1.02 is still officially built for Minecraft 1.5.2, but we’ve also released a separate 1.02 download for Minecraft 1.6.4 as a public beta.

If you are directly installing qCraft, a licensed copy of Minecraft is still required, as is a version-appropriate installation of Forge.

# A matter of perspective…

When designing the qCraft mod, we decided to highlight three concepts: Observational dependency, superposition and quantum entanglement. In the mod, there are two basic types of new blocks one can craft: observer dependent blocks (ODB) and quantum blocks (QB). The former represent classical blocks with a hint of quantumness, whereas the latter represent fully quantum objects.

The purpose of ODBs within the mod is twofold: First, to provide the classical background upon which quantum mechanical behavior can be contrasted. Second, to create exciting new structures within Minecraft that do not fall prey to the intrinsic randomness of quantum mechanics.

So, what exactly is an ODB?

An ODB is like a coin: it simply looks different (heads or tails) depending on your point of view. When two ODBs are “entangled”, it is like having two coins that are either both heads or both tails. No matter how far apart you take the two coins, unless you flip one of them, they will always look the same when viewed from above or below. Even if you give one of these coins to a friend and ask them to look at it at random, you will know what they see if they tell you the direction from which they looked at the coin. The same would be true for two dice, or two ODBs in Minecraft. There is nothing spooky about this.

The one weird feature of ODBs that is absent from dice and coins is this: once you look at an ODB from a new point of view, the block will not change its properties unless you look away and look again from a different point of view – for a coin or die, you will see something different once you look from a different point of view, even if you were looking at the objects the whole time. This feature of ODBs starts hinting at the following simple, but powerful truth about our world: We are not passive observers in a universe that evolves around us. We are part of the universe and as such, the line between observer and observed is blurred.

But as I mentioned above, ODBs are not quantum. What are they missing, then? They are missing the element of quantum superposition. Quantum what? An explanation will have to wait until next time. In the meantime, here is an animation on what is quantum, to whet your appetite.