theory.toys – Which-Path Environment

Environment Coupling

Coupling Strength g: 1.0 Environment Separation θ: 90°

Evolution

Time: 0.00 Animate

Visualization

Show density matrix Show Bloch sphere

Show environment states🔑 Unlock

Decoherence Metrics

          Purity Tr(ρ²): 1.000

          Coherence |ρ₀₁|: 0.500

          Concurrence: 0.000

          Env. Overlap ⟨E₀|E₁⟩: 0.000

About This Toy

A qubit starts in superposition (|0⟩ + |1⟩)/√2. Each path entangles with environment "pointer states" |E₀⟩ and |E₁⟩. As these environment states become orthogonal, the qubit's reduced density matrix loses coherence—interference disappears even without measuring. This is decoherence: quantum information leaks into inaccessible degrees of freedom.

Key insight: The environment "measures" which path the qubit took, destroying interference without anyone looking at the measurement result.