An entangled state can be either a pure state or a mixed state, depending on the specific situation.
Pure Entangled State: A pure entangled state is a quantum state that cannot be expressed as a product of individual states for the constituent systems. It describes a state of maximal entanglement and is typically represented by a superposition of entangled states. Pure entangled states have precise correlations between the subsystems and exhibit non-classical behavior. Examples of pure entangled states include the Bell states in quantum mechanics.
Mixed Entangled State: A mixed entangled state, also known as a mixed state, is a statistical ensemble of different pure states. It arises when there is uncertainty or lack of knowledge about the quantum state of the system. Mixed entangled states can be described by density matrices, which are positive semidefinite matrices that represent the probabilities of finding the system in different pure states. Mixed entangled states exhibit less pronounced correlations and may have classical counterparts. An example of a mixed entangled state is a statistical mixture of pure entangled states.
It is important to note that entanglement itself is a characteristic of the quantum state and does not depend on whether the state is pure or mixed. Both pure and mixed states can exhibit entanglement, but the nature and properties of entanglement may differ between the two types of states.