functions.php

<?php

// Allow logged-in user see private posts in 

add_action('pre_get_posts','filter_search');
function filter_Search($query){
    if( is_admin() || ! $query->is_main_query() ) return;
    if( current_user_can('edit_private_posts') ) {
        $query->set('post_status',array('private','publish'));
    }
}

?>