Blochgömb

Blochgömb is a theoretical construct in quantum mechanics. It is a geometrical representation of the state of a two-level quantum system, such as a qubit. The surface of the Blochgömb is a sphere, and any point on this sphere corresponds to a unique quantum state.

The north pole of the Blochgömb typically represents the state |0⟩, and the south pole represents the state |1⟩. Any other point on the sphere represents a superposition of these two states. The coordinates of a point on the Blochgömb are determined by the expectation values of the Pauli operators. Specifically, a state |ψ⟩ can be represented by a vector (x, y, z) on the Blochgömb, where x = ⟨ψ|σx|ψ⟩, y = ⟨ψ|σy|ψ⟩, and z = ⟨ψ|σz|ψ⟩. Here, σx, σy, and σz are the Pauli matrices.

The Blochgömb provides a convenient way to visualize quantum states and their evolution. Rotations of the Bloch vector correspond to unitary transformations of the quantum state. For example, applying a Hadamard gate to a qubit in the |0⟩ state moves its Bloch vector from the north pole to the equator. The Blochgömb is a fundamental tool for understanding and manipulating qubits in quantum computing and other quantum information processing tasks. It helps in understanding the concept of superposition and entanglement, and how these phenomena can be represented geometrically.