Here's a regex that almost works, but it leaves empty shards. Hence, grep...

local $_= q(one "two three" four five "six seven eight" nine);
my @foo = grep {$_} /\G(?:(\w+)\s*)|(?:"([^"]*)"\s*)/g;
local $,="\n";
print @foo, $/;
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It works for your data, but I suspect it is very fragile.