Watching people teletransport themselves in Star Trek is fun. But is it possible? And how long would it take?
To get some idea of how long it would take, suppose you were to teletransport yourself at broadband speed, say 100MBPS. For ease of calculation let one atom be transmitted by 1 byre, or 8 bits.
A typical human might weigh 70 kg. Taking a typical atom to weigh  
\[2 \times 10^{-26} \: kg\]
, a typical person contains about  
\[\frac{70}{2 \times 10^{-26}}=3.5 \times 10^{27}\]
This number of atoms could be transmitted in  
\[\frac{3.5 \times 10^{27}}{110^{8}/8}=2.8 \times 10^{20} \: seconds\]
This is equivalent to  
\[\frac{2.8 \times 10^{20}}{60 \times 60 \times 24 \times 365}=8.9 \times 10^{12} \: years\]
This is about 700 times longer than the age of the Universe, so teletransportation would appear impractical. We can compress the data. The human body is made up of about  
\[5 \times 10^{12}\]
  almost identical cells, so we can transmit the information for one cell, with some extra information for the location and tissue type of each cell in the body. We can also increase the broadband speed. If we could increase the broadband speed to 1,000GBPS, 10,000 times faster than 100MBPS, we could send the data in  
\[\frac{28 \times 10^{20}}{5 \times 10^{12} \times 10,000}=5600 \: seconds\]

Increasing broadband speed or finding more ways to compress the data could make it practical.