No, entangled quantum computers cannot be used for instantaneous real-time communication over large distances, such as between Earth and Mars. The reason for this limitation lies in the principles of quantum mechanics and the phenomenon known as the no-communication theorem.
Entanglement is a phenomenon where two or more quantum particles, such as qubits, become correlated in such a way that the state of one particle is dependent on the state of the other, regardless of the distance between them. However, entanglement does not allow for the transfer of classical information or communication faster than the speed of light.
The no-communication theorem, a fundamental principle in quantum information theory, states that it is impossible to use entanglement to transmit information faster than the speed of light. This means that even if two qubits on Earth and Mars were entangled, they cannot be used for instantaneous communication between the two locations.
When measurements are made on an entangled system, the measurement outcomes are random and do not reveal information until the results are communicated conventionally at light speed, which is the maximum speed at which information can be transmitted. Therefore, any communication between the two entangled quantum computers would still be limited by the speed of light, resulting in a delay corresponding to the distance between Earth and Mars.
While entanglement has important implications for quantum information processing, such as quantum teleportation and quantum key distribution, it does not violate the principles of causality or allow for faster-than-light communication.