Bell State
Steps
Circuit
Initial State
Both qubits start in the |0⟩ state.
What's happening?
The system begins in the computational basis state |00⟩, meaning both qubits are definitely in state |0⟩.
Key Insight
This is the default starting state for quantum computers.
Bloch Spheres
Note: Individual Bloch spheres cannot fully represent entangled states.
Probabilities
Statevector |ψ⟩
| State | Amplitude | |ψ| | Phase | Prob |
|---|---|---|---|---|
| |00⟩ | 1 | 1.000 | 0 | 100% |
| |01⟩ | 0 | 0.000 | — | 0% |
| |10⟩ | 0 | 0.000 | — | 0% |
| |11⟩ | 0 | 0.000 | — | 0% |
Algorithm Overview
Create a maximally entangled two-qubit state, the foundation of quantum entanglement.
Classical Approach
Classically, two bits can be correlated but not entangled. If you flip a coin and put the result in two envelopes, opening one tells you about the other — but the correlation was fixed when you sealed them. Quantum entanglement is different: the outcomes are truly undetermined until measurement.
Quantum Advantage
Bell states are the foundation of quantum communication protocols like teleportation and superdense coding. They enable secure key distribution (quantum cryptography) and demonstrate non-locality — correlations that cannot be explained by classical physics.
Complexity
Circuit depth: 2, Gate count: 2 (1 single-qubit, 1 two-qubit)
Applications
- •Quantum teleportation
- •Superdense coding
- •Quantum key distribution (QKD)
- •Bell inequality tests
- •Quantum error correction
Try it yourself
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