To simplify matters, let us assume that one could supply one's meal through an airtight hatch.
The plants would then only need to provide one's oxygen. If he spent all his time eating and dozing, one would need about 350 liters of oxygen per day (the amount of oxygen in 1.7 cubic meters of air). This much oxygen is produced in full sunlight by typical vegetation covering a floor area of between 5 and 20 square meters. Using the most productive "C4 plants" such as sugar cane, you could reduce the area needed to2.5 square meters. The victim would exhale 350 liters of carbon dioxide per day, which would enable the plants to grow with an increase of dry weight of 430 grams per day.
Now let's muddy the waters. If one's windows plus artificial lights supply 10% of full sunlight, multiply the required area of greenery by a factor of 10. If the lights go out at night, double the area--more in winter. Plants photosynthesize during the day more rapidly than they respire at night. Therefore, as a reasonable approximation, you can neglect the extra oxygen that plants consume at night.
If you don't intend to feed the victim, but hope he will survive by eating the plants, remember most material a plant synthesizes is indigestable, so double the area again. The inedible parts of the plants plus the person's feces would need to be decomposed or burnt to carbon dioxide to recycle the carbon they contain. So, if the person is a well-trained plant physiologist, this ambitious biosphere might need to be a plant-filled room about 20 square meters.
Basis of calculations:
Daily energy requirement of an adult dozing is 1750 kilocalories/day.
Energy content of 100 grams of sucrose is 400 kilocalories.
Therefore an adult needs 1750/400 = 438 grams of sucrose per day = 1.28 moles
sucrose per day.
Respiration of this requires 1.28 x 12 = 15.36 moles of oxygen per day. (One mole occupies 22.4 liters, so this correspond so 15.36 x 22.4 = 344 liters of pure oxygen per day.)
Photosynthesis rates of plants in the field under optimal lighting are between 10 and 30 micromoles (up to 70 in C4
plants) of carbon dioxide fixed per square meter per second (0.86 to 6.05 moles per square metre per day). For each mole of carbon dioxide the plants fix, they liberate a mole of oxygen.
Therefore the area required is somewhere between 18 square meters for the less productive plants down to 2.5 square meters for C4
Source: Stephen Fry - Institute for Cell and Molecular Biology - Edinburgh University
adapted from a submission to The NewScientist - The Last Word