Quantum Foundations: Relativity, Gravity, and Geometry

A relativistic representation of the qubit is presented in which pure states live on the lightcone and mixed states live in the time-like interior of the lightcone. Unitary time evolution and non-unitary measurements are recast as Lorentz transformations. Continuously monitoring a qubit can mix rotations and boosts, producing quantum state trajectories equivalent to the energy-momentum streamlines of a classical charge in a stochastic electromagnetic field. In particular, for a superconducting qubit monitored by homodyne readout, the orthogonal quadratures carry information corresponding precisely to the backaction due to rotations and boosts. Unlike for a classical charge, however, the choice of amplified quadrature, and thus the type of Lorentz transformation, can be delayed until long after the interaction between the qubit and probe field. The future choice therefore seems to affect past dynamics.