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QKD 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 how can we measure that QKD is secure? In terms of what? and how can it be clearly proved? Is it possible by code it in any programming language like Java? well I am still looking for a good research topic under this area.

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  • $\begingroup$ I assume you've read the Wikipedia article? It's clear from your question that you're not familiar with cryptography, or quantum computing, so it's hard to give a good answer. There's too much to cover. Your best bet for learning more is to read a cryptography textbook or watch a university course in cryptography on youtube or something. $\endgroup$ – Craig Gidney Jun 27 '16 at 18:57
  • $\begingroup$ The scientific "proof" of security is that nobody has broken it. There is no other kind of "proof" in science. $\endgroup$ – CuriousOne Jun 27 '16 at 19:57
  • $\begingroup$ Basically the 'security' here means that the QKD can distribute the key to the two parties, while the third party can only reveal/destroy the information with a very low probability. $\endgroup$ – XXDD Jun 28 '16 at 3:13
  • $\begingroup$ It's a very nice technology for an ideal world. Is it the ours remains a nice question too $\endgroup$ – user46925 Jul 20 '16 at 9:45
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The security of QKD is based on the quantum mechanics related theorem, including uncertainty relations and no-cloning theorem. If there is a third person wants to eavesdrop the information, the action would change the quantum state which could be detected by the legal users.

The security of QKD protocols has been proven, for example in publication "Simple Proof of Security of the BB84 Quantum Key Distribution Protocol" PRL 85,441(2000).

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Modern security proofs of QKD are based on information theory. Specifically, it measures the amount of entropy present between the communicating parties, i.e. if the entropy between Alice and Bob is less than the entropy between Alice and Eve, then the protocol can be deemed secure. Now, in order to get a visible statistic, there are equations that compute the key rate based on entropy of the parties.

A good survey paper is this one by Scarani et al.

To answer your second question, yes, it's possible to simulate the theoretical bounds in different languages. However, in my experience, it's often convex optimizations.

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