Include in std::regex search, exclude from std::sub_match using std::regex_token_iterator

I want to tokenize a std::string using \s (space), \r (carriage return), \t (tab), and \n (new line) as delimiters, but between a pair of quotes no delimiters should be considered and no other quotes should be allowed. To achieve this, I use the following regex (represented as a raw string literal):

R"((\"[^\"]*\")|[^\n\r\s\t]+)"

which gives the following output when used as the std::regex of a std::sregex_token_iterator:

Test sample [Try It Online]:

#include <iostream>
#include <algorithm>
#include <iterator>
#include <regex>

int main() {
   std::string text = "Quick \"\"\"\" \"brown fox\".";
   std::regex re(R"((\"[^\"]*\")|[^\n\r\s\t]+)");
   std::copy(std::sregex_token_iterator(text.cbegin(), text.cend(), re, 0),
             std::sregex_token_iterator(),
             std::ostream_iterator<std::string>(std::cout, "\n"));
}

Test output:

Quick
""
""
"brown fox"
.

This results in the inclusion of the surrounding quotes in the sub matches. Instead, I want to get rid of these surrounding quotes. To do so, I can obviously modify the iterated sub matches manually, but I wonder if it is possible and how one can achieve to eliminate the surrounding quotes using the std::regex and the std::sregex_token_iterator?