QProcess : error and state doesn't change

#include "PythonDetector.h"
#include <QProcess>
#include <iostream>
#include <QApplication>
#include <QTest>PythonDetector::PythonDetector(QObject *parent) : QObject(parent)
{}void PythonDetector::detect()
{
    bool state;
    QString path = "";
    QString  command("python3");
    QStringList params;    command = "time";
    params << "sleep" << "1";
    QProcess *process = new QProcess();
    connect(process, SIGNAL(errorOccurred(QProcess::ProcessError)), this, SLOT(errorOccurred(QProcess::ProcessError)));
    connect(process, SIGNAL(stateChanged(QProcess::ProcessState)), this, SLOT(stateChanged(QProcess::ProcessState)));
    std::cout << "Starting. Last Error=" << process->error()<< ", current State= " << process->state() << std::endl;
    state=process->startDetached(command, params, path);
    std::cout << "Waiting for start. StartDetached state=" << state <<" => Last Error=" << process->error()<< ", current State= " << process->state() << std::endl;
    qApp->processEvents();
    state = process->waitForStarted(-1);
    qApp->processEvents();
    std::cout << "Waiting for finish. Started state=" << state <<" => Last Error=" << process->error()<< ", current State= " << process->state() << std::endl;
    while(!process->waitForFinished(-1)){
        std::cout << "Waiting for finish. Finished state=" << state <<" => Last Error=" << process->error()<< ", current State= " << process->state() << std::endl;
        qApp->processEvents();
        QTest::qWait(1000);
    }
    //process->close();
    std::cout << "End of process" << std::endl;}
void PythonDetector::errorOccurred(QProcess::ProcessError error)
{
    std::cout << "Error : " << error << std::endl;
}
void PythonDetector::stateChanged(QProcess::ProcessState newState)
{
    std::cout << "State : " << newState << std::endl;
}

MainWindow::MainWindow(){
..
QTimer::singleShot(100,this, SLOT(test()));
..
}

void MainWindow::test()
{
    PythonDetector detector;
    detector.detect();
}

Starting. Last Error=5, current State= 0
Waiting for start. StartDetached state=1 => Last Error=5, current State= 0
Waiting for finish. Started state=0 => Last Error=5, current State= 0
Waiting for finish. Finished state=0 => Last Error=5, current State= 0
Waiting for finish. Finished state=0 => Last Error=5, current State= 0
0.00user 0.00system 0:01.00elapsed 0%CPU (0avgtext+0avgdata 2132maxresident)k
0inputs+0outputs (0major+77minor)pagefaults 0swaps
Waiting for finish. Finished state=0 => Last Error=5, current State= 0
Waiting for finish. Finished state=0 => Last Error=5, current State= 0
...