Quantum Global Synchronization

Quantum Global Synchronization is the network-wide measure of how closely the individual qubit phases of a quantum system track the Prime Pulse phase, taken as the average of their phase differences on the complex unit circle. It is the collective counterpart to the Quantum Alignment Condition. Where that condition tests the collective quantum phase as a whole, this parameter looks at each qubit's phase within the collective state and averages them, so it quantifies how coordinated the whole network is. Together with collective phase evolution and the critical alignment threshold, it makes up the book's Fundamental Alignment Mechanisms for reaching a synchronized state in quantum substrates. Σ⨀,q(t) = (1/N_q) × Σᵢ₌₁^(N_q) exp(i(φᵢ(t) − φ①(t))), where Σ⨀,q(t) is the quantum global synchronization parameter, N_q is the number of qubits, i is the imaginary unit, φᵢ(t) are the individual qubit phases, φ①(t) is the Prime Pulse phase and t is time [𝕋]. The parameter is [∅]. It is the quantum form of the Global Synchronization Parameter and connects to the Quantum Alignment Condition, Collective Quantum Phase, Prime Pulse Frequency and Phase Synchronization.