A qubit is a slice of a complex ray and the metaplectic lift is the origin of complex probability

Quantum information theory conventionally treats the discrete-variable (DV) qubit as an irreducible ontological primitive residing in a complex Hilbert space. In this work, we propose a geometric-symplectic alternative where the qubit is a projective slice of a continuous, deterministic "parent ray" evolving in the Siegel upper half-space Hn. We demonstrate that the Bloch sphere arises as a physical manifestation of the Hopf fibration S1 → S3 → S2 resulting from the constraint of minimal symplectic area. Crucially, we identify the metaplectic lift—the double cover of the symplectic group Sp(2n, R)—as the fundamental physical origin of complex probability amplitudes, providing the geometric necessity for the imaginary unit and the physical action exp(iS/ħ). We prove that the Siegel metric identifies the parent ray as the geometry of physical distinguishability. By invoking Gromov’s non-squeezing theorem, we derive logical discreteness from the impossibility of compressing the parent ray beyond the ħ/2 "needle eye" of measurement. We introduce the "Wigner hull" to extend this framework to non-Gaussian states and provide a consistency proof for the Born rule based on symplectic volume. Finally, we detail the symplectic geometric processor (SGP) and the "geometric echo" protocol, presenting the Siegel distinguishability benchmark: a mathematical shortcut where many-body fidelity is calculated as a constant-depth O(1) metric distance, bypassing the exponential sampling overhead of conventional architectures. Numerical simulations confirm a strict monotonic correspondence between the Siegel metric distance and quantum fidelity, validating the benchmark as a reliable proxy for logical state health.