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--- quantum-state [August 22, 2026 at 22:11] – Ivan Janevski
+++ quantum-state [August 26, 2026 at 15:46] (current) – external edit 127.0.0.1
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-# Quantum State
+# Quantum state
-**Quantum states** describe the complete information content of a quantum system. Like classical bits, qubits occupy definite states; unlike classical bits, qubits can exist in superposition—a linear combination of basis states. A quantum state is represented as a vector $|\psi\rangle$ in a complex Hilbert space, normalized so $\langle\psi|\psi\rangle = 1$.
+**Quantum states** describe the complete information content of a quantum system. Like classical bits, qubits occupy definite states; unlike classical bits, qubits can exist in superposition—a linear combination of basis states. A quantum state of $n$ qubits is represented as a vector $|\psi\rangle$ in a complex Hilbert space $\mathbb{C}^{2^n}$, normalized so $\langle\psi|\psi\rangle = 1$.
 A single-qubit state can be written $|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$ where $|\alpha|^2 + |\beta|^2 = 1$. Multi-qubit states live in tensor products of qubit spaces. Entangled states cannot be factored into independent qubits—they exhibit non-local correlations measured by entropy or purity.