How about losing the duplicates while sorting? Here is the quicksort implementation from Rosetta Code:

sub quick_sort {
    my @a = @_;
    return @a if @a < 2;
    my $p = pop @a;
    quick_sort(grep $_ < $p, @a), $p, quick_sort(grep $_ >= $p, @a);
}
 
my @a = (4, 65, 2, -31, 0, 99, 83, 782, 1);
@a = quick_sort @a;
print "@a\n";
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(This is for sorting numbers.) If you now replace >= with > so you get

quick_sort(grep $_ < $p, @a), $p, quick_sort(grep $_ > $p, @a);
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you will get a sorted array without duplicates.