Quantum Key Distribution
 Unstructured QKD
Most QKD protocols that we analyze today have a high symmetry in signals and measurements. Key rate calculations are basically multiparameter optimization with a nonlinear objective function. The symmetry of QKD protocols allows us often to perform this optimization analytically. However, imperfections in experimental realizations often break the symmetry: Think for example at beamsplitters that do not have exact 50/50 splitting ratios, detectors that differ in their detection efficiency. Many protocols also have too many parameters, even if some symmetry persists. This often includes protocol implementations with sidechannels (see below).Our group develops methods that allow to calculate canonically secret key rates for arbitrary QKD protocols. This method is based on the theory of convex optimization and allows for efficient numerical evaluations.
Recent Publications:
Unstructured quantum key distribution
This paper lays the foundation of our approach and makes use of the dual formulation of the convex problem of secret key rate calculations. This publication forms the basis of our QKD Security Analysis Software and is best suitable for entanglementbased QKD protocols.
 Reliable numerical key rates for quantum key distribution
Adam Winick, Norbert Lütkenhaus, Patrick J. Coles
arXiv/1710.05511
This approach is based on the primal problem formulation of the secret key rate problem and leads to more stable results for prepare and measure QKD protocols.

 SideChannel
 Network QKD
 Development of Optical Protocols
Quantum Repeater
 Analysis of Quantum Repeater Architectures
What architectures should Quantum Repeaters eventually have to avoid conceptional bottlenecks in their development? We work closely with the groups of Liang Jiang (Yale) and Jungsang Kim (Duke) on this question.
Recent Publications: S. Muralidharan, J. Kim, N. Lütkenhaus, M. D. Lukin, L. Jiang, Ultrafast and faulttolerant quantum communication across long distances
Phys. Rev. Letters, Vol. 112, 250501 (2014)  S. Muralidharan, L. Li, J. Kim, N. Lütkenhaus, M.D. Lukin, L. Jiang, Efficient long distance quantum communication, Nature Scientific Reports 6, 20463, (2016)
 R. Namiki, L. Jiang, J. Kim, N. Lütkenhaus; “Role of syndrome information on a oneway quantum repeater using teleportationbased error correction”, Phys. Rev. A 94, 052304 (2016)
 S. Muralidharan, J. Kim, N. Lütkenhaus, M. D. Lukin, L. Jiang, Ultrafast and faulttolerant quantum communication across long distances
 Beating the repeaterless bounds for lossy bosonic channels
The repeaterless bounds (TGW14, PLOB15) gives an upper bound on how much secret key per mode we can get by using lossy bosonic channels (freespace links, optical fiber). The goal of a quantum repeater is to design setups that use lossy bosonic channels, but augments them by intermediate repeater stations and classical communication channels between the stations. The goal is to do better than to send signals directly through the lossy bosonic channels without the repeater stations.
Our particular interest is to find out what is the simplest setup to beat this bound, no matter what the distance is. Note that we are not particularly interested whether the resulting secret key rate scales polynomially or exponentially, as long as it is better than what the repeaterless bounds offers. Our research approaches this question from both sides: nogo theorems to identify what does not work, and specific protocols that tell us what works.Recent Publications: Could Gaussian regenerative stations act as quantum repeaters?
R. Namiki, O. Gittsovich, S. Guha, N. Lütkenhaus Phys Rev. A 90, 062316 (2014)
 Overcoming lossy channel bounds using a single quantum repeater node
David Luong, Liang Jiang, Jungsang Kim, Norbert Lütkenhaus
Appl. Phys. B, 122:96 (2016)
 Could Gaussian regenerative stations act as quantum repeaters?
Quantum Communication & Information Complexity
 Optical Implementations of Protocols with Quantum Advantage
We are working on protocols that show a quantitative quantum advantage over classical protocols and can be implemented with simple optical tools such as laser pulses and threshold detectors.
Recent Publications: J.M. Arrazola, N. Lütkenhaus, Quantum fingerprinting with coherent states and a constant mean number of photons, Phys. Rev. A, 89, 062305 (2014)
Here we give an optical version of the quantum finger printing protocol which allows actual implementations for large input sizes and tolerates transmission loss, detection loss, mode mismatch at beamsplitters and detector dark counts.  J. M. Arrazola, N. Lütkenhaus, Quantum Communication with Coherent States and Linear Optics, Phys. Rev. A, 90, 042335 (2014)
We generalize our approach of translating qubitbased complexity based protocols to protocols based on coherent states and linear optics.  Feihu Xu,Juan Miguel Arrazola, Kejin Wei, Wenyuan Wang, Pablo PalaciosAvila, Chen Feng, Shihan Sajeed, Norbert Lütkenhaus, HoiKwong Lo; Experimental quantum fingerprinting with weak coherent states,
Nature Communications 6, 8735, (2015)
The first demonstration of our 2014 protocol! It realizes a quantum advantage over the best known classical communication protocol solving the comparison of two databases in the simultaneous message passing model without shared randomness! We work with input sizes of 10^8 and more bits.  J.M. Arrazola, M Karasamanis, N. Lütkenhaus, Practical quantum retrieval games, Phys Rev A 93 062311 (2016)
 J. M. Arrazola, D. Touchette, Quantum Advantage on Information Leakage for Equality, arXiv:1607.07516
In this manuscript it is shown that our quantum fingerprinting protocol does not only have a communication complexity advantage, but also a information complexity advantage! Our optical quantum protocol leaks less information to the referee than any classical protocol could.
 J.M. Arrazola, N. Lütkenhaus, Quantum fingerprinting with coherent states and a constant mean number of photons, Phys. Rev. A, 89, 062305 (2014)
 Network Applications
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