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)...

states. Mixed states can be represented by points inside the Bloch sphere (or in the Bloch ball). A mixed qubit state has three degrees of freedom: the...

other disciplines that depend on analysis and geometry, such as the Bloch sphere of quantum mechanics and in other branches of physics. The extended complex...

Poincaré sphere may refer to: Poincaré sphere (optics), a graphical tool for visualizing different types of polarized light Bloch sphere, a related tool...

equate, respectively, to a rotation around the x, y and z axes of the Bloch sphere by π {\displaystyle \pi } radians. The Pauli-X gate is the quantum equivalent...

viewed as the precession of the state vector on the Bloch sphere. The representation on the Bloch sphere for a state vector ψ ( 0 ) {\displaystyle \psi (0)}...

adiabatic pulse sequence that takes the atom on a trajectory around the Bloch sphere and back. The levels pick up a phase on this trip due to the so-called...

(or density operators) of the quantum space C2, whose boundary is the Bloch sphere. The Jones vectors correspond to the underlying space C2, that is, the...

\Delta _{\lambda }} can be interpreted as a uniform contraction of the Bloch sphere, parameterized by λ {\displaystyle \lambda } . In the case where λ =...

there would be many angles through which state vectors would flip on the Bloch sphere. There would be an optimal length in the Rabi setup that would give the...

states on the surface of the Bloch sphere to mixed states within the Bloch sphere. This would contract the Bloch sphere by some finite amount and the...

Poincaré sphere to the real plane). A dynamical pseudospin skyrmion results from the stereographic projection of a rotating polariton Bloch sphere in the...

qubit parameters. A single qubit gate is achieved by rotation in the Bloch sphere. Rotations between different energy levels of a single qubit are induced...

terms of the identity matrix and the Pauli matrices also leads to the Bloch sphere representation of 2 × 2 mixed states’ density matrix, (positive semidefinite...

around the positive z-axis in state space, which may be visualized as a Bloch sphere. At a time t {\displaystyle t} and a frequency ω {\displaystyle \omega...

discrete), a qubit is continuous-valued, describable by a direction on the Bloch sphere. Despite being continuously valued in this way, a qubit is the smallest...

These concepts are illustrated in the table below, where the sphere represents the Bloch sphere, the arrow represents the state of the atom, and the hand...

and has infinite order. In quantum mechanics, the Riemann sphere is known as the Bloch sphere, and the Hopf fibration describes the topological structure...

is a rotation of the Bloch sphere, the Haar measure for spin-1/2 particles is invariant under all rotations of the Bloch sphere. This implies that the...

}|1\rangle \langle 1|} This map is a rotation about the Z-axis of the Bloch sphere by an angle α {\displaystyle \alpha } . For α = π {\displaystyle \alpha...

states are represented by points in the interior. This is known as the Bloch sphere picture of qubit state space. An example of pure and mixed states is...

Poincaré sphere (but of radius P), as shown in the accompanying diagram. In quantum mechanics and computing, a related concept is the Bloch sphere. Often...

Quantum Mission". 2024-09-30. Inside India’s National Quantum Mission. Bloch Sphere. 2024. Retrieved 4 July 2025. "National Quantum Mission: India's Quantum...

circles in S3 ". Versors have been used to represent rotations of the Bloch sphere with quaternion multiplication. The facility of versors illustrate elliptic...

{C} \mathbf {P} ^{1}} , the complex projective line, also known as the Bloch sphere. It is complex, because a quantum-mechanical wave function has a complex...

n-dimensional Bloch sphere. This can be seen as related to linear inversion giving states which lie outside the valid space (the Bloch sphere). MLE in these...

\mathbb {C} \mathbf {P} ^{1}} . This is known as the Bloch sphere or, equivalently, the Riemann sphere. See Hopf fibration for details of the projectivization...

Bloch sphere representation of states (in blue) and optimal POVM (in red) for unambiguous quantum state discrimination on the states | ψ ⟩ = | 0 ⟩ {\displaystyle...

Bloch sphere representation of a qubit. The state | ψ ⟩ = α | 0 ⟩ + β | 1 ⟩ {\displaystyle |\psi \rangle =\alpha |0\rangle +\beta |1\rangle } is a point...

Gelfand–Naimark–Segal construction for more details. Atomic electron transition Bloch sphere Greenberger–Horne–Zeilinger state Ground state Introduction to quantum...