Why is the problem infeasible?

Given $mathbf V_t=mathbf v_tmathbf v_t^H$ where $mathbf v_t=left(e^{jtheta_{1}},e^{jtheta_{2}}right)^H$:
begin{equation*}
begin{array}{ll}
underset{mathbf V}{operatorname{minimize}} & 1
text { subject to } & operatorname{diag}(mathbf V)=1
&|mathbf V|_*-operatorname{trace}left[boldsymbollambdaboldsymbollambda^Hleft(mathbf V-mathbf V_tright)right]-|mathbf V_t|_2leq 0
end{array}
end{equation*}
where $|bullet|_*$ and $|bullet|_2$ is the nuclear norm and 2-norm. $boldsymbollambda$ is the leading eigenvector of $mathbf V_t$.

Since $mathbf V=mathbf V_t$ is a feasible solution, the optimization problem is feasible. Why does CVX show the problem is infeasible?

clear;clc;close all;

Vt = rand(2,1);
Vt = (exp(1i*Vt)*exp(1i*Vt)');
[lambda,~] = eigs(Vt,1,'largestabs');
cvx_begin sdp
    variable V(2,2) hermitian semidefinite
    minimize(1)
    subject to
        diag(V) == 1
        norm_nuc(V) - real(trace(lambda*lambda'*(V-Vt))) - norm(Vt,2) <= 0
cvx_end