# Bit corresponds to postion? Sign corresponds to mometum?

Hi! I was going through the lectures on Quantum Mechanics and Quantum Computation by Umesh Vazirani. In one of his lectures he defines the quantum state of a two energy level system in |0> , |1> basis where |0> corresponds to ground state and |1> corresponds to excited state. Then he defines another orthonormal basis |+> | – > where |+> equals (1/sqrt2) |0 > + (1/sqrt2) |1> and | – > equals (1/sqrt2) |0 > – (1/sqrt2) |1>. He goes on saying that when measurement is made in |0> |1> basis we are measuring the BIT and when measurement in done in |+> | – > basis we are measuring  SIGN. Then he adds that ” in a sense BIT corresponds to position and SIGN corresponds to momentum“, which left me confused. What does he mean by that? Was it just meant as an analogy to Heisenberg’s Uncertainty principle?

Asked on June 26, 2019 in

When I looked up these lectures, I found this link https://www.classcentral.com/course/edx-quantum-mechanics-and-quantum-computation-613.

To help us out, can you tell us where in the lectures he makes this specific statement?  The Heisenberg Uncertainty Principle is usually introduced in the form of it being “impossible to know both the position and the momentum of a particle with absolute accuracy”.  However, many systems of interest for quantum computing are not based on moving particles, but on the spin of particles, where the uncertainty principle manifests itself a different way.