Not that easy with a regex. You could split on " and search only in every second chunk. This only works if " does not occur escaped. inside a field.

Ah, I see you got better advice in the Chatterbox with Text::CSV

Try using something like Text::CSV or the like and let it handle the nastiness of parsing the CSV-y data for you (just tell it to use \t as the delimiter rather than a comma) then do your diddling on the chunks it returns.

$inputstring=qq{field1\tfield2\t"field3\t\t"\tfield4\t"field5\t\t"\n};

you would not want to strip the tabs surrounding field4 even though it is surrounded by quotation marks. A regular expression like s/^([^"]*"[^\t"]*)\t+/$1/ would strip the tabs from the first quoted field, but not from all fields. You could wrap that in a while loop and swap the first character class to allow for paired quotes

while (s/^((?:[^"]|"[^"]*")*"[^\t"]*)\t+/$1/){1}

but CSV also includes an escape character, and any escaped quotation marks would then break the above. So why fight with all that when there is a well-tested solution at your fingertips?

You seriously might wish to consider ... a brute-force loop.   Initialize a string-index, and initialize an in_quotes flag to false.   While that index has not yet passed the end of the string, look for a quote-mark or a tab.   A quote-mark flips the value of the in_quotes flag.   A tab, if in_quotes, is removed and the loop is restarted without incrementing the index (i.e. next) because the string just shrank and we don’t want to overlook any characters.

Seriously... you won’t go home and tell your significant other “honey, let me tell you about the amazing algorithm I designed today,” but it will do the job perfectly well.

Code?

$str = join "", map {my $_ = $_; /^"/ && s/\t+//g; $_} $str =~ /"[^"]*
+"|[^"]*/g;
[download]

Here's a regex solution. Single-quotes are used in place of double-quotes to avoid Windoze command-line escape-ology, but this approach will work with double-quotes just as well. Note: All quotes must be paired. Quoted sub-strings can contain escaped quotes.

>perl -wMstrict -le
"my $string =
   qq{uuu\tvvv\t'www\t\t'\txxx\t'\t\tyyy'\tzzz\n};
 print qq{$string};
 ;;
 $string =~
   s{ ( ' [^\\']* (?: \\. [^\\']*)* ' )        }
    { (my $notabs = $1) =~ tr{\t}{}d;  $notabs }xmsge;
 ;;
 print qq{$string};
"
uuu     vvv     'www            '       xxx     '               yyy'  
+  zzz

uuu     vvv     'www'   xxx     'yyy'   zzz
[download]

Update: This version ignores escaped double-quotes both inside and outside paired-quoted sub-strings:

use warnings;
use strict;

# check with escaped double-quotes inside and outside
# double-quoted sub-strings.

my $string =
  qq{uuu\t\\"vvv\t"notab\t\t"\txxxx\t"\t\tno\\"tab"\tzzz\n};
print qq{$string};

$string =~
  s{ ((?<! \\) " [^\\"]* (?: \\. [^\\"]*)* ") }
   { (my $notabs = $1) =~ tr{\t}{}d;  $notabs }xmsge;

print qq{$string};
[download]

Output:

uuu     \"vvv   "notab          "       xxxx    "               no\"ta
+b"        zzz
uuu     \"vvv   "notab" xxxx    "no\"tab"       zzz
[download]

As has already been stated, Text::CSV is the most robust solutionf or this type or problem:

use Text::CSV;

use strict;
use warnings;

my $inputstring = qq{field1\tfield2\t\"field3\t\t\"\tfield4\n};

my $csv = Text::CSV->new({eol => "\n", sep_char => "\t", binary => 1})
+;

$csv->parse($inputstring)
    or die "csv error: " . $csv->error_input();
my @columns = $csv->fields();

s/\t//g for (@columns);

$csv->combine(@columns)
    or die "csv error: " . $csv->error_input();
my $string = $csv->string();

print $string;
[download]

Here's the regex solution though using double quotes that allow escaped quotes

my $inputstring = qq{field1\tfield2\t\"field3\t\t\"\tfield4\n};

$inputstring =~ s{("(?: (?> [^\"\\]+ ) | \\ . )*")}{ (my $str = $1) =~
+ s/\t//g; $str }xesg;

print $inputstring;
[download]