Insights of quantum time for quantum evolution

If time is emergent, quantum system is entangled with quantum time as it evolves. If the system contains entanglement within itself, which we can call \textit{internal entanglement} to distinguish it from the ``external" time-system entanglement, the speed of evolution is enhanced. In this paper, we explore the insights of quantum time for the evolution of a system that contains two entangled qubits. We consider two cases: (1) two initially entangled qubits that evolve under local dynamics; (2) two interacting qubits such that entanglement between them is generated over time. In both cases, the key message is that increasing internal entanglement speeds up the evolution and makes the system more entangled with time. This result could be useful to gain new insights of quantum time for black hole evaporation or cosmological perturbations in an expanding Universe, because we also have an evolving entangled bipartite system in those cases.