Learn about the 4 most common types of quantum states in this article: pure, mixed, entangled, and coherent states. Discover their unique properties and applications.
4 Most Common Types of Quantum States
Quantum mechanics is a branch of physics that studies the behavior of matter and energy at the atomic and subatomic level. One of the fundamental principles of quantum mechanics is that particles can exist in a superposition of multiple states. These states can be categorized into four main types, which we will discuss in this article.
1. Pure States
A pure quantum state is a state that describes the properties of a single quantum system. It is represented by a vector in a complex vector space called Hilbert space. The vector represents the state of the quantum system, and it can be written as a linear combination of basis vectors. A basis is a set of orthogonal vectors that span the Hilbert space. The coefficients of the linear combination are complex numbers, and they represent the probability amplitudes of measuring the system in a particular state.
For example, a qubit is a two-level quantum system that can be in a superposition of two states, which we can represent as |0⟩ and |1⟩. A pure state of a qubit can be written as a linear combination of these two states:
|ψ⟩ = α|0⟩ + β|1⟩,
where α and β are complex numbers that satisfy the normalization condition |α|^2 + |β|^2 = 1.
2. Mixed States
A mixed quantum state is a statistical ensemble of pure states. It is a combination of different pure states, each with a certain probability of occurrence. A mixed state cannot be represented by a single vector in Hilbert space. Instead, it is represented by a density matrix, which is a positive-semidefinite, Hermitian operator.
For example, consider a qubit that is in the pure state |ψ⟩ = α|0⟩ + β|1⟩ with probability p and in the pure state |φ⟩ = γ|0⟩ + δ|1⟩ with probability 1-p. The density matrix of the mixed state is:
ρ = p|ψ⟩⟨ψ| + (1-p)|φ⟩⟨φ|,
where |ψ⟩⟨ψ| and |φ⟩⟨φ| are projection operators that project onto the subspaces spanned by |ψ⟩ and |φ⟩, respectively.
3. Entangled States
An entangled state is a pure quantum state that describes the properties of a composite quantum system. It is a state in which the properties of the individual subsystems cannot be described independently of each other. In other words, the subsystems are correlated in a way that cannot be explained classically.
For example, consider a two-qubit system that is in the entangled state:
|ψ⟩ = α|00⟩ + β|11⟩,
where |00⟩, |01⟩, |10⟩, and |11⟩ are the four basis states of the two-qubit system. If we measure the first qubit and obtain the result |0⟩, the state of the second qubit collapses to |0⟩ with probability |α|^2 and to |1⟩ with probability |β|^2. The measurement of the first qubit affects the state of the second qubit, even if the two qubits are far apart.
4. Coherent States
A coherent state is a quantum state that is closely related to classical waves. It is a superposition of different number states, each with a fixed phase relationship. Coherent states have many interesting properties, such as a minimum uncertainty in position and momentum, and they are used in many applications of quantum mechanics,
