Added Tr[rhoAB] == 1 constraint when no rhoA is given for BasicKeyRateFunc.

Added note to the pauliBasis function reminding people that the phase conventions differ from bloch sphere rotations.

Author: JBurniston

keyRateModules/BasicKeyRateFunc.m

@@ -27,7 +27,9 @@
 %   Bob's measurements that line up with it's corresponding observable in
 %   observablesJoint. These values should be betwen 0 and 1.
 % * rhoA (nan): The fixed known density matrix on Alice's side for
-%   prepare-and-measure protocols.
+%   prepare-and-measure protocols. Setting to nan means this is ignored and
+%   no rhoA constraint is passed to the convex solver. Furthermore, an
+%   explicit Tr[rhoAB] == 1 constraint is added in its place.
 % Outputs:
 % * keyrate: Key rate of the QKD protocol measured in bits per block
 %   processed.
@@ -113,16 +115,19 @@
 %operators for the key map (Z).
 mathSolverInput.krausOps = params.krausOps;
 mathSolverInput.keyProj = params.keyProj;
-% also include rhoA from the description if it was given
-if ~isequaln(params.rhoA,nan)
-    mathSolverInput.rhoA = params.rhoA;
-end
 
 numObs = numel(params.observablesJoint);
 
 mathSolverInput.equalityConstraints = arrayfun(@(x)...
     EqualityConstraint(params.observablesJoint{x},params.expectationsJoint(x)),1:numObs);
 
+% Include rhoA (if given) or add an explicit Tr[rhoAB] == 1 constriant.
+if ~isequaln(params.rhoA,nan)
+    mathSolverInput.rhoA = params.rhoA;
+else
+    mathSolverInput.equalityConstraints(end+1) = EqualityConstraint(eye(params.dimA*params.dimB),1);
+end
+
 % if block diag information was give, then pass it to the solver.
 if ~isequaln(params.blockDimsA,nan)
     mathSolverInput.blockDimsA = params.blockDimsA;

tools/HelperFunctions/pauliBasis.m

@@ -3,12 +3,18 @@
 % states of the Pauli Z operator (H/1,V/2) to the eigen states of the Pauli
 % X (D/+,A/-) or Y (R,L) operators.
 %
+% Note: Unlike, the functions present in Rotations, Qudit, and Coherent
+% which are based on rotations around the bloch sphere, pauliBasis does not
+% pick up any additional phase factors.
+%
 % Inputs:
 % * basis: Integer which selects which basis the unitary should transform
 %   the Z eigen basis to: 1=Z (H/1,V/2) (identity), 2=X (D/+,A/-), 3=Y (R,L).
 % * revY (false): Logical to reverse the assignement for the Pauli Y eigen
 %   vectors. In other words, revY = true: U|1> = |R>, U|2> = |L>, revY =
 %   false: U|1> = |L>, U|2> = |R>. Has no effect for other basis choices.
+%
+% See also: Rotations, Qudit, Coherent
 arguments
     basis (1,1) double {mustBeMember(basis,[1,2,3])}
     revY (1,1) logical  = false