Finite-key effects in multipartite quantum key distribution protocols

We analyze the security of two multipartite quantum key distribution (QKD) protocols, specifically we introduce an $N$-partite version of the BB84 protocol and we discuss the $N$-partite six-state protocol proposed in arXiv:1612.05585v2. The security analysis proceeds from the generalization of known results in bipartite QKD to the multipartite scenario, and takes into account finite resources. In this context we derive a computable expression for the achievable key rate of both protocols by employing the best-known strategies: the uncertainty relation and the postselection technique. We compare the performances of the two protocols both for finite resources and infinitely many signals.

[1]  Hermann Kampermann,et al.  Secret key rates for coherent attacks , 2012, 1207.0085.

[2]  Renato Renner,et al.  Cryptographic security of quantum key distribution , 2014, ArXiv.

[3]  Renato Renner,et al.  Security of quantum key distribution , 2005, Ausgezeichnete Informatikdissertationen.

[4]  Thomas Vidick,et al.  Practical device-independent quantum cryptography via entropy accumulation , 2018, Nature Communications.

[5]  D. Bruß.  Optimal Eavesdropping in Quantum Cryptography with Six States , 1998, quant-ph/9805019.

[6]  Umesh Vazirani,et al.  Fully device-independent quantum key distribution. , 2012, 1210.1810.

[7]  R. Renner,et al.  Uncertainty relation for smooth entropies. , 2010, Physical review letters.

[8]  Marco Tomamichel,et al.  Quantum Information Processing with Finite Resources - Mathematical Foundations , 2015, ArXiv.

[9]  Renato Renner,et al.  Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way postprocessing. , 2007, Physical review letters.

[10]  Michael Epping,et al.  Multi-partite entanglement can speed up quantum key distribution in networks , 2016, 1612.05585.

[11]  Bing Qi,et al.  Practical challenges in quantum key distribution , 2016, npj Quantum Information.

[12]  Ardehali.  Bell inequalities with a magnitude of violation that grows exponentially with the number of particles. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[13]  Thomas Holenstein,et al.  On the Randomness of Independent Experiments , 2006, IEEE Transactions on Information Theory.

[14]  Matthias Christandl,et al.  Postselection technique for quantum channels with applications to quantum cryptography. , 2008, Physical review letters.

[15]  Serge Fehr,et al.  Sampling in a Quantum Population, and Applications , 2009, CRYPTO.

[16]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[17]  V. Scarani,et al.  The security of practical quantum key distribution , 2008, 0802.4155.

[18]  S. Wehner,et al.  Fully device-independent conference key agreement , 2017, 1708.00798.

[19]  Marco Tomamichel,et al.  A Fully Quantum Asymptotic Equipartition Property , 2008, IEEE Transactions on Information Theory.

[20]  Hermann Kampermann,et al.  Min-entropy and quantum key distribution: Nonzero key rates for ``small'' numbers of signals , 2011 .

[21]  A. V. Belinskii,et al.  Interference of light and Bell's theorem , 1993 .

[22]  Kiel T. Williams,et al.  Extreme quantum entanglement in a superposition of macroscopically distinct states. , 1990, Physical review letters.

[23]  V. Scarani,et al.  Finite-key security against coherent attacks in quantum key distribution , 2010, 1008.2596.

[24]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[25]  Marco Tomamichel,et al.  Duality Between Smooth Min- and Max-Entropies , 2009, IEEE Transactions on Information Theory.

[26]  Marco Tomamichel,et al.  Tight finite-key analysis for quantum cryptography , 2011, Nature Communications.