When two quantum systems, such as qubits, are entangled, the state of the combined system cannot be described independently in terms of the individual states of the subsystems. In other words, after entanglement, the quantum state of the joint system is no longer separable into the states of the individual subsystems. Instead, the entire entangled system must be described by a single quantum state that encompasses both subsystems.
In the scenario you described, Alice prepares a qubit in system A, and Bob prepares a qubit in system B. When these qubits are entangled, the resulting combined system is described by a joint quantum state that represents the entanglement between the two qubits.
The specific quantum state of the entangled system depends on the nature of the entangling operation performed on the qubits. The resulting state can be a superposition of various states that exhibit correlations and dependencies between the two qubits. These correlations can manifest in a variety of ways, such as entanglement in spin, polarization, or other properties of the qubits.
To summarize, after entanglement, neither Alice nor Bob possess independent quantum states that describe their respective qubits. Instead, they collectively possess a single entangled quantum state that describes the joint system of the entangled qubits. The properties and behavior of this joint quantum state depend on the specific entanglement operation performed on the qubits.