Bit commitment, two blobs with same bit, without revealing it? Suppose we have bit commitment scheme:
$n=p*q$ and $t \in QNR_n$, with Jacobi $(\frac{t}{n})=1$

Commitment(P), random $x\in \mathbb{Z}_n$, $y=x^2t^b$, where $b$ is bit.

Ok, suppose we have $y_1$ and $y_2$ blobs containing same $b$

How P can prove that both blobs contain same bit without revealing it?
Give a zero-knowledge proof that $y_1 \times y_2$ is a Quadratic Residue.

[Extra verbage included because a one line answer feels too brief]

If we have $y_1 = x_1^2 t^{b_1}$ and $y_2 = x_2^2 t^{b_2}$, then $y_1 y_2 = (x_1x_2)^2 t^{b_1 + b_2}$.

If $b_1 = b_2$, this product is either $(x_1x_2)^2$ (if $b_1 = b_2 = 0$), or $(x_1x_2t)^2$ (if $b_1 = b_2 = 1$), in both cases a Quadratic Residue.

If $b_1 \ne b_2$, this product is $(x_1x_2)^2 t$, which is a Quadratic Nonresidue, hence we would not be able to generate a Zero Knowledge Proof that it is.