Overview

Classical bits are 0 or 1. Quantum bits (qubits) can be 0, 1, or both at the same time. This changes the rules of information.

Core Idea

Superposition: A qubit exists in a state $\alpha|0\rangle + \beta|1\rangle$. It contains more “potential” information than a bit, but when you measure it, it collapses to 0 or 1.

Formal Definition (if applicable)

Entanglement: “Spooky action at a distance.” Two qubits can be linked so that measuring one instantly determines the state of the other, even if they are light-years apart.

Intuition

  • No-Cloning Theorem: You cannot copy a qubit. (If you could, you could violate the uncertainty principle). This makes quantum money theoretically impossible to counterfeit.
  • Quantum Teleportation: Moving the state of a qubit to another location (destroying the original).

Examples

  • Quantum Key Distribution (BB84): Using physics to detect eavesdroppers. If Eve tries to measure the key, she disturbs the state (Heisenberg Uncertainty), and Alice and Bob know they are being watched.
  • Shor’s Algorithm: A quantum computer can factor large numbers exponentially faster than a classical computer, breaking RSA encryption.

Common Misconceptions

  • “Quantum computers try every answer at once.” (Not quite. They use interference to cancel out wrong answers and amplify the right one).
  • “Faster than light communication.” (Entanglement cannot transmit information faster than light. You still need a classical channel to decode the result).
  • Von Neumann Entropy: The quantum version of Shannon entropy.
  • Decoherence: The environment messing up the quantum state (why quantum computers are hard to build).

Applications

  • Cryptography: Post-quantum crypto.
  • Simulation: Simulating molecules for drug discovery.

Criticism / Limitations

Quantum computers are extremely fragile and error-prone (Noise).

Further Reading

  • Nielsen & Chuang, Quantum Computation and Quantum Information
  • Wilde, Quantum Information Theory