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Tensor products
Two qubits live in a four-dimensional state space with basis |00⟩, |01⟩, |10⟩, |11⟩. The tensor product combines individual systems. With n qubits, the pure state has 2ⁿ amplitudes.
State-space growth is exponential, but readable classical output remains limited.
Separable and entangled states
A separable state can be factored into individual qubit states. The Bell state (|00⟩+|11⟩)/√2 cannot. Measuring one qubit produces correlations with the other.
Entanglement is joint structure, not a communication channel.
Density matrices and partial trace
Density matrices represent pure and mixed states and allow subsystem analysis. Taking the partial trace of an entangled Bell state yields a maximally mixed single-qubit state.
A globally pure entangled state can produce locally mixed subsystems.
Applied activity
Complete a simulator or analysis exercise: reproduce the lesson's central example, record assumptions and outputs, and explain one source of error or limitation.
Read the full lesson text
1. Tensor products
Two qubits live in a four-dimensional state space with basis |00⟩, |01⟩, |10⟩, |11⟩. The tensor product combines individual systems. With n qubits, the pure state has 2ⁿ amplitudes.
State-space growth is exponential, but readable classical output remains limited.
2. Separable and entangled states
A separable state can be factored into individual qubit states. The Bell state (|00⟩+|11⟩)/√2 cannot. Measuring one qubit produces correlations with the other.
Entanglement is joint structure, not a communication channel.
3. Density matrices and partial trace
Density matrices represent pure and mixed states and allow subsystem analysis. Taking the partial trace of an entangled Bell state yields a maximally mixed single-qubit state.
A globally pure entangled state can produce locally mixed subsystems.
4. Applied activity
Complete a simulator or analysis exercise: reproduce the lesson's central example, record assumptions and outputs, and explain one source of error or limitation.
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