No, it is not possible to create an entangled pair of qubits across a distance using purely classical communication. The creation and manipulation of entangled states require quantum mechanical principles and operations.
Entanglement is a fundamental concept in quantum mechanics, where the state of two or more particles becomes correlated in such a way that the state of one particle cannot be described independently of the other particles. Creating an entangled pair of qubits typically involves performing a quantum operation, such as an entangling gate, on a pair of qubits that are initially in a separable state.
Classical communication, which involves transmitting information using classical bits, cannot create or transmit quantum entanglement. Classical communication is limited to transmitting classical information and cannot replicate the non-local correlations exhibited by entangled quantum states.
To create entanglement between two qubits separated by a distance, quantum communication methods such as entanglement swapping or quantum teleportation are typically employed. These methods utilize quantum entanglement as a resource to transmit the quantum state or entanglement from one location to another.
In summary, classical communication alone cannot create entangled pairs of qubits across a distance. Quantum communication is necessary to establish the required entanglement between the qubits.