ZipArchive creates invalid ZIP file

I found the—in hindsight, obvious—error in my code. The ZipArchive has to be disposed to make it write its content to its underlying stream. So I had to save the stream to a file after the end of the using block of the ZipArchive.
And it was important to set the leaveOpen argument of its constructor to true, to make it not close the underlying stream. So here is the complete working solution:

using (MemoryStream zipStream = new MemoryStream())
{
    using (ZipArchive zip = new ZipArchive(zipStream, ZipArchiveMode.Create, true))
    {
        var entry = zip.CreateEntry("test.txt");
        using (StreamWriter sw = new StreamWriter(entry.Open()))
        {
            sw.WriteLine(
                "Etiam eros nunc, hendrerit nec malesuada vitae, pretium at ligula.");
        }
    }

    var file = await Windows.Storage.ApplicationData.Current.LocalFolder.CreateFileAsync(
        "test.zip",
        CreationCollisionOption.ReplaceExisting);

    zipStream.Position = 0;
    using (Stream s = await file.OpenStreamForWriteAsync())
    {
        zipStream.CopyTo(s);
    }
}

On all of your Stream Object you must rewind the streams from the beggining in order from them to be read correctly by other applications using the .Seek method.

Example:

zipStream.Seek(0, SeekOrigin.Begin);