How we filter the search base on post-meta tags

Thats because you got the meta_query wrong. Check documentation in Codex

Your query should be:

$args = array(
            'posts_per_page' => 30,
            'paged' => $paged, 
            'post_type' => 'post', 
            'post_status' => 'publish',
            'meta_query' => array(
                                array(
                                 'key' => 'post_state',
                                 'value' => $stateName,
                                 'compare' => '=' // not necesary by default is "="
                                )
                            ) 
            );

Basically you need to pass inside the meta_query array, another array with the key and value. Also $stateName should be a var.