Validation error for complex SDPs

[catch22]

See here. This code

% prepare Ψ ⊗ Ψ for a Haar random pure state Ψ
[U, ~, ~] = svd(rand(3) + 1i*rand(3));
sigma = U * diag([1 0 0]) * U';
sigma = sigma / trace(sigma);
rho = kron(sigma, sigma);
dims = [3 3];

% try to find 2:1 extension that is 1:0-PPT
[RHO_EXT, ~, ~, ~, INFO] = sym_extension(rho, dims, [2 1], [1 0], [1 1], 'sdpt3');

leads to the following error:

error: total dimension of C should be > length(b)
error: called from
 validate at line 143 column 5
 sqlp at line 159 column 38
 solve_sdp>solve_sdp_with_sdpt3 at line 201 column 17
 solve_sdp at line 177 column 3
 sym_extension at line 120 column 14

Currently the workaround is to comment out line 143 in validate.m.
(This does not work, see below!)

[catch22]

Here is another instance of this bug from @dragomang87:

[rho, dims] = horodecki_state_24(0.5);
U = kron([1 0; 0 i],eye(4));
rho = U * rho * U';
[~, ~, ~, ~, info] = sym_extension(rho, dims, [2 1], [1 0], [1 1], 'sdpt3');

[catch22]

Some further investigations with regards to the original problem case:

It turns out that, after commenting out the relevant line in validate.m, SDPT3 reports that the problem is infeasible:

[U, ~, ~] = svd(rand(3) + 1i*rand(3));
sigma = U * diag([1 0 0]) * U';
sigma = sigma / trace(sigma);
rho = kron(sigma, sigma);
dims = [3 3];
[RHO_EXT, ~, ~, ~, INFO] = sym_extension(rho, dims, [2 1], [1 0], [1 1], 'sdpt3');

=>

... sqlp stop: primal problem is suspected of being infeasible...

But of course it should not be infeasible since we are trying to extend a product state.
If we comment back in the line in validate.m and we remove the PPT constraint then we obtain:

[RHO_EXT, ~, ~, ~, INFO] = sym_extension(rho, dims, [2 1], [0 0], [1 1], 'sdpt3');

=>

... sqlp stop: primal problem is suspected of being infeasible...

which is again incorrect.

On the other hand, if we work with orthogonal O then everything works fine:

[O, ~, ~] = svd(rand(3));
sigma = O * diag([1 0 0]) * O';
sigma = sigma / trace(sigma);
rho = kron(sigma, sigma);
dims = [3 3];
[RHO_EXT, ~, ~, ~, INFO] = sym_extension(rho, dims, [2 1], [1 0], [1 1], 'sdpt3');

and

[RHO_EXT, ~, ~, ~, INFO] = sym_extension(rho, dims, [2 1], [0 0], [1 1], 'sdpt3');

This points towards a real problem in the handling of complex SDPs, not just a bug in the validation code.