Journal
Long-form notes, Qiskit experiments, and applied optimization thinking.
A step-by-step study of Bernhardt's example showing how an initially unentangled pair of qubits becomes the Bell state through a CNOT gate, beginning with the tensor product and following the calculation explicitly.
Read note →Entanglement becomes much clearer when we stop treating it only as a factorization test and start asking what Alice and Bob actually observe when they measure. This note develops the Bell-state measurement behavior step by step, showing why same-basis measurements are perfectly correlated while different-basis measurements become 50/50.
Read note →Tensor products answer a basic question in quantum mechanics: how do we describe two quantum systems together? This note develops tensor products from scratch, shows why two qubits require a four-dimensional joint state space, and explains why a pure two-qubit state is entangled when it cannot be factored into separate pure states for Alice and Bob.
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