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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.
Đọc toàn bộ nội dung bài học
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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