Computational 00 (|00⟩)

Computational 00 state |00⟩ is the product of two ground state qubits, the default initial state on most quantum computers. It is a separable (unentangled) state and an eigenstate of both Z₁ and Z₂ operators with eigenvalue +1.

$$|00\rangle = |0\rangle_1 \otimes |0\rangle_2 = \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix}$$

in the computational basis ordering (|00⟩, |01⟩, |10⟩, |11⟩).

• Separable: factorizes into independent single-qubit states
• Product state: no entanglement between qubits
• Z eigenstates: Z₁|00⟩ = |00⟩, Z₂|00⟩ = |00⟩ (both with eigenvalue +1)
• Pure state: purity = 1, zero entropy
• Initial state: default state after quantum computer initialization

• Ground state: represents both qubits in their lowest energy level
• Measurement outcome: measured in Z basis yields 00 with certainty
• Basis state: building block for superpositions and entangled states
• Reference: starting point for quantum algorithms (usually initialized via reset to |0⟩ on both qubits)

Prepare by:

1. Initialize both qubits to ground state (automatic on startup or via reset gate)
2. Measure both qubits in Z basis: outcomes are always 0, 0
3. Apply no gates (identity operation)

• Single-qubit: tensor product of two zero states
• One-qubit excitation: Computational 01 or Computational 10
• Two-qubit excitation: Computational 11
• Bell states: |00⟩ is a component of Bell 00 (|Φ⁺⟩) and Bell 11 (|Φ⁻⟩)

Measuring |00⟩ in the computational (Z) basis always yields outcome 00. Measuring in other bases (X or Y) requires rotating both qubits first.