Spooky Action at a Distance

Entanglement

What Is Entanglement?

Entanglement is a quantum phenomenon where two or more qubits become correlated in such a way that the state of one instantly affects the state of the other, regardless of distance.

Einstein famously called it "spooky action at a distance" because he found it troubling. But experiments have confirmed it's real.

When qubits are entangled, measuring one immediately determines the outcome of measuring the other, even if they're on opposite sides of the universe.

Interactive Bell State

Click a qubit to measure it. Watch how measuring one instantly determines the other!

Qubit A
⚡
entangled
Qubit B
|Φ+⟩ = (|00⟩ + |11⟩) / √2

Creating Entanglement

The most common entangled state is the Bell state, created with a Hadamard gate followed by a CNOT (controlled-NOT) gate:

|Φ+⟩ = (|00⟩ + |11⟩) / √2

This state says: "The two qubits will always have the same value when measured—both 0 or both 1—but which one is random."

Why It's Not Magic

No Faster-Than-Light Communication

You can't use entanglement to send messages. The measurement outcomes are random; you can only verify the correlation after classical communication.

It's About Correlation

The "spookiness" is that the correlation exists even though neither qubit had a predetermined value. It's decided at measurement time, for both, instantly.

Why Entanglement Matters

Exponential State Space

Entangled qubits can represent correlations that would require exponentially many classical bits to describe. This is the source of quantum advantage.

Quantum Algorithms

Every major quantum algorithm (Shor's, Grover's, etc.) relies on entanglement to create correlations that enable speedups.

Quantum Communication

Entanglement enables quantum key distribution (QKD) for secure communication and quantum teleportation of quantum states.

The CNOT Gate

The CNOT (Controlled-NOT) gate is the key to creating entanglement:

  • It operates on two qubits: a control and a target
  • If control is |1⟩, it flips the target
  • If control is |0⟩, it does nothing
  • When the control is in superposition, it creates entanglement
Terminal Log

$ cat recovered_note.txt Breakthrough: chaining gates creates circuits. The order matters. Must document the full pipeline.

A

GNTNAGLMENET

Hint: Unscramble: Einstein's 'spooky action'

Reflection Questions

  • 1If entanglement doesn't allow faster-than-light communication, what makes it useful for computation?
  • 2How does entanglement differ from classical correlation (like two coins that always match)?
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