Learn about the five most common types of entangled states in quantum mechanics, including the Bell state, GHZ state, W state, Cluster state, and Cat state, and their applications in quantum computing, communication, and cryptography.
5 Most Common Types of Entangled States
Entangled states are a fundamental concept in quantum mechanics. In simple terms, entangled states are a pair or a group of quantum particles that share a quantum state, meaning they are intrinsically connected even if separated by large distances. When one particle is measured, the state of the other particle is instantly determined, regardless of the distance between them. This phenomenon is known as quantum entanglement and is a crucial aspect of quantum computing and communication. There are several types of entangled states, but here we will discuss the five most common ones:
1. Bell State
The Bell state, also known as the EPR (Einstein-Podolsky-Rosen) pair, is the most well-known entangled state. It consists of two quantum bits (qubits) that are in a superposition of two possible states, where the outcome of measuring one particle determines the state of the other. The four possible Bell states are:
- Φ⁺ state: (|00⟩+|11⟩)/√2
- Φ⁻ state: (|00⟩-|11⟩)/√2
- Ψ⁺ state: (|01⟩+|10⟩)/√2
- Ψ⁻ state: (|01⟩-|10⟩)/√2
Where |0⟩ and |1⟩ represent the two possible states of a qubit.
2. GHZ State
The GHZ (Greenberger-Horne-Zeilinger) state consists of three or more qubits that are entangled such that the outcome of measuring any one of them determines the state of all the others. The three-qubit GHZ state is:
(|000⟩+|111⟩)/√2
3. W State
The W state is a three-qubit entangled state where two of the qubits are in the same state, and the third qubit is in a different state. The W state is:
(|001⟩+|010⟩+|100⟩)/√3
4. Cluster State
The Cluster state is a graph state consisting of a group of qubits that are connected to each other in a specific way. The Cluster state is particularly useful for quantum computing because it enables universal quantum computation through a process called measurement-based quantum computing. The simplest Cluster state is the 1D cluster state, which consists of a linear chain of qubits, and its state is:
|+⟩⊗n = (|0⟩+|1⟩)/√2 ⊗ n
5. Cat State
The Cat state is a two-qubit entangled state that is in a superposition of two macroscopically distinguishable states, such as the two states of a cat being dead or alive. The Cat state is:
(|00⟩+|11⟩)(|00⟩-|11⟩)/2
These are the five most common types of entangled states in quantum mechanics. Each of them has unique properties and applications in quantum computing, communication, and
