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[Predefined]

## Functions | |

State | QubitSpinState (double x, double y, double z) |

Returns a J=1/2 pure state so that <X>=`x` , <Y>=`y` , and <Z>=`z` , up to normalization. | |

State | ZPlus () |

Returns the +1 eigenstate of SigmaZ. | |

State | ZMinus () |

Returns the -1 eigenstate of SigmaZ. | |

State | XPlus () |

Returns the +1 eigenstate of SigmaX. | |

State | XMinus () |

Returns the -1 eigenstate of SigmaX. | |

State | YPlus () |

Returns the +1 eigenstate of SigmaY. | |

State | YMinus () |

Returns the -1 eigenstate of SigmaY. | |

State | QubitMUBState (itype i) |

Returns the `i` th state from the 6-element qubit MUB set: {|0>, |1>, |+>, |->, |+i>, |-i>}. | |

State | QubitSICPState (itype i) |

Returns the `i` th state from a 4-element qubit SICPOVM chosen so that the 1st is |0>, and the 2nd is in the X-Z plane. | |

Operator | Identity (itype D) |

Returns the identity operator in `D` dimensions. | |

Operator | Zero (itype D) |

Returns the zero operator in `D` dimensions. | |

Operator | QubitSpinOperator (double x, double y, double z) |

Returns an arbitrary J=1/2 spin operator . | |

Operator | Hadamard () |

Returns the Hadamard matrix for qubits. | |

Operator | HalfPhase () |

Returns the phase-flip matrix (square root of SigmaZ) for qubits. | |

Operator | SigmaI () |

Returns the J=1/2 Identity operator. | |

Operator | SigmaX () |

Returns the J=1/2 Pauli spin operator along the X axis. | |

Operator | SigmaY () |

Returns the J=1/2 Pauli spin operator along the Y axis. | |

Operator | SigmaZ () |

Returns the J=1/2 Pauli spin operator along the Z axis. | |

Operator | Sigma (itype i) |

Returns the `i` th matrix from the Pauli group, {X,Y,Z,I}. | |

Operator | Jz (itype d) |

Returns the Jz (angular momentum along the z-axis) operator in `d` dimensions. | |

Operator | Jx (itype d) |

Returns the Jz (angular momentum along the z-axis) operator in `d` dimensions. | |

Operator | Jy (itype d) |

Returns the Jz (angular momentum along the z-axis) operator in `d` dimensions. | |

Operator | Jn (itype d, double x, double y, double z) |

Returns the `d` -dimensional angular-momentum-along-the-(x,y,z)-axis operator. |

The ConstStates namespace contains pre-defined states and operators that are frequently used in quantum information processing. These include:

- the identity and zero matrices in all dimensions [Identity(d), Zero(d)],
- the Hadamard (Fourier transform) operator for qubits [Hadamard()],
- the phase gate (square root of SigmaZ) operator for qubits [HalfPhase()],
- the qubit Pauli operators [Sigma{X,Y,Z,I}(), Sigma(i)],
- all the Pauli operators' eigenstates [{X,Y,Z}{Plus,Minus}(), QubitMUBState(i)],
- the J=1/2 spin-along-an-arbitrary-vector operator [QubitSpinOperator(x,y,z)],
- the J=1/2 spin-along-an-arbitrary-unit-vector state [QubitSpinState(x,y,z)],
- the four states making up a canonical symmetric informationally complete POVM for qubits [QubitSICPState(i)]
- the J=(d-1)/2 angular momentum operators [J{x,y,z}(d)]
- the J=(d-1)/2 angular-momentum-along-an-arbitrary-vector operator [Jn(d,x,y,z)]

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