In other words the water in the vase would have to contain less minerals/electrolytes/ions and sugars than are found inside the flower stem. By the process of osmosis, water will move from a less concentrated solution to a more concentrated solution as the electrolytes/ions/minerals try to move from a more concentrated area (stems) to a less concentrated area (vase).
Your option then is to fill the vase with ultra-pure water. The common option is to buy distilled water, although ultrapure water is face cleaner than distilled water. For the record, ultrapure water is 18 times cleaner than triple-distilled water. Not to fret however, because within a cut flower the osmotic pressure difference using distilled versus ultrapure is negligible.
So, how effective is a purer water in extending the vigor of cut flowers? Save your money and enjoy the flowers while they are fresh. #wateristhenewgold