Quantum entanglement links qubits so their combined state cannot be described as independent states, making individual measurement outcomes dependent. It enables conditional transformations and therefore nontrivial quantum computation. section 1.3 section 4.2.1
Use product and nonproduct states to distinguish independence from entanglement:
- A product state combines two single-qubit states; its measurement outcomes are independent, like two independent biased coins. section 4.2.1
- A nonproduct state cannot be factored into independent single-qubit states; its qubits are entangled and their measurement outcomes are linked. section 4.2.1
- Entanglement is essential for meaningful quantum computing but can increase processing demands and coherence costs. section 4.2.1
Bell states
The state [√0.5, 0, 0, √0.5] permits only matching outcomes, 00 and 11, each with probability 0.5. The other Bell states similarly encode linked two-qubit outcomes through sign or position changes. section 4.2.1
bell_state1 = [sqrt(0.5), 0.0, 0.0, sqrt(0.5)] bell_state2 = [sqrt(0.5), 0.0, 0.0, -sqrt(0.5)]
Inspect Python state-vector definitions for the first two Bell states. section 4.2.1
