Bloch sphere

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In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), named after the physicist Felix Bloch. Mathematically each quantum mechanical system is associated with a separable complex Hilbert space H {\displaystyle H} . A pure state of a quantum system is represented by a non-zero vector ψ {\displaystyle \psi } in H {\displaystyle H} . The vectors ψ {\displaystyle \psi } and λ ψ {\displaystyle \lambda \psi } (with λ {\displaystyle \lambda } a non-zero complex number) represent the same state. A system with n mutually orthogonal quantum states can be described by a Hilbert space of dimension n. Pure states can be represented...

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