Quantum Superposition Calculator

Quantum states are described by complex probability amplitudes, not probabilities themselves, because amplitudes can interfere -- add constructively or destructively -- in a way plain probabilities cannot. The calculator squares the normalized amplitudes to give you State 1 Probability and State 2 Probability, but it needs the amplitudes first to correctly compute the Interference Term and Visibility, which depend on the amplitudes' relative phase, not just their magnitudes.

State 1 Probability and State 2 Probability come from squaring the normalized amplitudes alone -- the phase term only enters once the two components are combined into the full superposition state, which is what the Interference Term, Superposition Magnitude, Visibility, and Phase Sensitivity outputs capture. The individual-state probabilities describe what you'd measure in the computational basis, where relative phase has no effect.

Visibility of 1 means the two amplitude components have exactly equal magnitude, producing maximum interference contrast -- the Interference Term swings through its full possible range as Phase Difference varies. Visibility of 0 means one amplitude has collapsed to zero, so there's effectively only one state left and no interference pattern to speak of, since interference requires two non-zero components to combine.

State 1 Probability and State 2 Probability each describe one component in isolation, while Coherence (the absolute product of both normalized amplitudes) specifically measures the cross-term that only exists because the system is in a genuine superposition rather than a classical mixture. Coherence is highest when both amplitudes are equal and falls toward zero as either one dominates, tracking how much quantum interference the state can actually exhibit.