Failed to redirect execvpe() stderr to file with dup2()

Question

As shown below, I want to redirect stderr from execvpe() to file. But the resulted /tmp/test does not contain expected content.

// redirect.cpp
#include <fcntl.h>
#include <errno.h>
#include <unistd.h>
#include <stdio.h>

int main()
{
    int fd = open("/tmp/test", O_RDWR | O_CREAT, S_IRUSR | S_IWUSR);
    if (fd != -1) {
        dup2(fd, 1);
        dup2(fd, 2);
        close(fd);
    }
    char* argv[] = {"ls-not-exist","-al","/etc/passwd",(char*)0};
    char* envp[] = {"PATH=/bin", 0};
    int ret = execvpe(argv[0],argv,envp); 
    printf("ret:%d %d\n", ret, errno);

    return 0;
}

My expected output is like

$ ls-not-exist -al /etc/passwd
ls-not-exist: command not found

But the actual output is

$ ./redirect; cat /tmp/test
ret:-1 2

which does not contain stderr content.

I also tried with other function(execvp()) in exec() family, but also failed.