# ConstStates Namespace Reference [Predefined]

Useful pre-defined (constant) objects for use in quantum info. More...

## 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 ith state from the 6-element qubit MUB set: {|0>, |1>, |+>, |->, |+i>, |-i>}.
State QubitSICPState (itype i)
Returns the ith 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 .
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 ith 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.

## Detailed Description

Useful pre-defined (constant) objects for use in quantum info.

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)]

Generated on Wed Jun 14 22:25:43 2006 for linalg by  1.4.4