Quantum mechanics challenges our everyday intuition. At its core lies the qubit – the quantum bit – which uses mathematical notation called Dirac ket notation to describe states.
Physicists denote the two basic states of a qubit as |0⟩ (ket 0) and |1⟩ (ket 1). These resemble classical bits (0 or 1 in computers), but quantum rules unlock far more power.
The Foundation: |0⟩ and |1⟩
A classical bit is either 0 or 1. A qubit starts in a definite state too:
- |0⟩ often represents the ground state (like an electron at lowest energy).
- |1⟩ represents the excited state.
We can write any pure basic state as |ψ⟩ = |0⟩ or |ψ⟩ = |1⟩.
Yet the magic begins when we go beyond these.
Superposition: Being in Two States at Once
A qubit can exist in a superposition – a linear combination of |0⟩ and |1⟩ simultaneously.
Mathematically: |ψ⟩ = α|0⟩ + β|1⟩
Here, α and β are complex numbers (amplitudes), and |α|² + |β|² = 1 (normalization – the total probability must be 100%).
This means the qubit is partly |0⟩ and partly |1⟩ until measured. Upon measurement, it “collapses” to |0⟩ with probability |α|² or |1⟩ with |β|².
A famous example is Schrödinger’s cat (thought experiment): the cat is in superposition of alive and dead until observed.
We visualize superposition on the Bloch sphere: |0⟩ at the north pole, |1⟩ at the south pole, and superpositions as points on the surface.
Superposition enables quantum computers to explore many possibilities simultaneously – the source of their potential speedup.
Entanglement: Spooky Action at a Distance
Entanglement takes quantum weirdness further. When two qubits become entangled, their states link inextricably – even across vast distances.
A common entangled state (Bell state): |ψ⟩ = (1/√2) (|00⟩ + |11⟩)
If you measure the first qubit as |0⟩, the second instantly becomes |0⟩ (and vice versa for |1⟩) – no matter how far apart.
Einstein called this “spooky action at a distance” because it seems to violate locality (information faster than light). However, quantum mechanics shows no information transfers faster than light – we can’t use it for instant communication.
Entanglement powers quantum cryptography, teleportation, and the exponential advantage in quantum computing.
Why It Matters
From simple |0⟩ and |1⟩, superposition lets qubits hold vast information in parallel. Entanglement correlates them in ways classical systems can’t replicate.
Together, they form the foundation of quantum technologies – from secure communication to solving impossible classical problems.
Quantum mechanics isn’t just theory; experiments confirm these phenomena daily. The universe operates on probabilities and connections deeper than we imagine.