what is the motivation behind quantum key distribution with Continuous variable? Quantum Key Distribution protocol is a technique that allow two parties to share common secret key for cryptographic purpose and defined as being secure, by definition. But I am still wondering what is the motivation behind quantum key distribution with Continuous variable ?
It's easier to work with a lot of photons in a stream than to work with a single photon at once.  This is explained in the paper introducing continuous-variable quantum key distribution.  (With apologies for the paywall.  Ms. Greene, tear down this wall!  Or read the arXiv preprint if you're not a rebel.)

P.S.  I originally answered the question as follows, with the above paragraph at the end, and the answer was accepted.  It spawned a long discussion in comments and chat, but, while it represents my perspective on the market for quantum key distribution products today in the context of information security and cryptography, it wasn't appropriate as an answer to the question as asked, about continuous-variable quantum key distribution in the context of the basic research program of quantum key distribution in physics.  I am leaving it here for context of the discussion:


  One word: money.
  
  Quantum key distribution networks serve no useful cryptographic purpose.
  
  
  They do not work without classical cryptography to authenticate the peers.
  The best speeds for quantum key distribution are measured at megabits per second rather than the gigabits per second achievable by classical cryptography on $100 mass-market CPUs.
  The widely advertised security guarantees founded on laws of physics are nonsense.
  
  
  But because rich governments are apparently easily bedazzled with mumbo-jumbo about laws of physics guaranteeing security, it is highly profitable for companies like ID Quantique and MagiQ Technologies to sell packages of snake oil at hundreds of thousands of dollars a pop.
  
  As for the specific case of continuous-variable systems...
  
  (Financial disclosure: I'm not getting a piece of the pie that ID Quantique and MagiQ Technologies are splitting.  But then I'm also not getting a piece of any pie in classical cryptography either.  In fact I'm pretty bereft of pie at the moment.)