# 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.

## Definition

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

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

## Properties

- **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

## Role in Quantum Computing

- **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)

## Construction

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)

## Relation to Other States

- Single-qubit: tensor product of two [[quantum-state-0|zero states]]
- One-qubit excitation: [[quantum-state-computational-01|Computational 01]] or [[quantum-state-computational-10|Computational 10]]
- Two-qubit excitation: [[quantum-state-computational-11|Computational 11]]
- Bell states: |00⟩ is a component of [[quantum-state-bell-00|Bell 00 (|Φ⁺⟩)]] and [[quantum-state-bell-11|Bell 11 (|Φ⁻⟩)]]

## Measurement

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