Quantum states within the computational basis $\{|0\rangle, |1\rangle\}$ are formally defined and represented either via Dirac notation (bra-ket formalism) or equivalent column vector representations in a complex Hilbert space. The core principle asserts that quantum state vectors obey standard linear algebraic rules of superposition, scalar multiplication distribution, and basis decomposition, allowing seamless translation between abstract kets and concrete matrix forms for theoretical manipulation. This concept establishes the foundational framework for Quantum Information Theory by defining how qubits are mathematically structured before logical operations such as gate transformations are applied.
Quantum states within the computational basis $\{|0\rangle, |1\rangle\}$ are formally defined and represented either via Dirac notation (bra-ket formalism) or equivalent column vector representations…