We propose various new techniques in quantum information theory, including a de Finetti style representation theorem for finite symmetric quantum states. As an application, we give a proof for the security of quantum key distribution which applies to arbitrary protocols.
Our new approach for proving the security of QKD has already found various applications. For example, it is used for the analysis of protocols based on continuous systems continuous variable QKD as well as to improve the analysis of known (practical) protocols practical implementation exploiting the fact that an adversary cannot control the noise in the physical devices owned by Alice and Bob (see, e.g., @cite_38 @cite_41 @cite_4 ).
@cite_41 @cite_38 @cite_4
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We present here an information theoretic study of Gaussian collective attacks on the continuous variable key distribution protocols based on Gaussian modulation of coherent states. These attacks, overlooked in previous security studies, give a finite advantage to the eavesdropper in the experimentally relevant lossy channel, but are not powerful enough to reduce the range of the reverse reconciliation protocols. Secret key rates are given for the ideal case where Bob performs optimal collective measurements, as well as for the realistic cases where he performs homodyne or heterodyne measurements. We also apply the generic security proof of Christiandl et. al. [quant-ph 0402131] to obtain unconditionally secure rates for these protocols. We study quantum key distribution with standard weak coherent states and show, rather counter-intuitively, that the detection events originated from vacua can contribute to secure key generation rate, over and above the best prior art result. Our proof is based on a communication complexity quantum memory argument.