- Quantum Key Distribution Theory Tools
We develop tools to improve quantum key distribution systems. One tool are computable upper bounds on the key rate for given experimental set-ups, both for one-way and two-way classical communication. We use this tool to work on improved classical communication protocols to increase the output of secret key from the date that are generated in experiments.
- Theory for practical quantum key distribution
In this line of research it has been the goal to close the gap between abstract security proofs that involve qubit signals and measurements, and real quantum-optical implementations. These work with typical signals such as laser pulses on the sender side, and photo-detectors monitoring complete optical modes on the other side. I developed security proofs starting with the restricted scenario of individual attacks. We then combined this approach with earlier work by Dominic Mayers to give an unconditional security proof. This proof not only gives the asymptotic limit, but also considers all finite-size effects of the key generation. Unfortunately, this results in a very dense presentation comprising already 40 pages, so that this paper is currently not published in a refereed journal. The basic idea of tagging is then taken up in the work with D. Gottesman, H-K Lo and J. Preskill, which focuses otherwise on imperfections on the side of sender and receiver. We show that such imperfections can be accounted for in the generation of the secret key as long as they can be bounded in a certain way. Note that only this line of research made it possible to claim unconditional security for today’s Quantum Key Distribution schemes.
- Continuous Variable QKD
One system we are interested in is a continuous variable QKD system which uses optical light pulses and homodyne or hetereodyne detection as measurements. In this particular set-up, coherent light pulses with a Gaussian distribution of amplitudes is sent and a heterodyne measurement performed. Our question addresses the practicability of this set-up and what methods should be used to turn the observed data into secret key. Issues of concern are especially the implementation of classical error correction codes which usually work not at the ideal regime. We have been showing that the best protocol combines two important ideas in continuous variable QKD in order to get a stable overall protocol: postselection of data and the so-called ‘reverse reconciliation’, which basically requires that the receiver, instead of the sender, getting active in the error correction stage. With ideal error correction at hand, reverse reconciliation would be sufficient. [M. Heid, N. Lütkenhaus, Phys. Rev. A, Vol. 76, 022313 (2007).]
- BB92 protocol with strong phase reference
- Verifying Quantumness of Devices:
Quantum mechanics allows us to change the nature of our communication systems. In this, we make use of channels for quantum signals, memories for quantum states, and more complex schemes such as teleportation of quantum states. Many experiments have been done to demonstrate the benefits coming from these tools, mostly done as proof of principle experiments. It is not always easy to formulate exactly what to demonstrate in order to prove that the presented device actually operates in the quantum regime as demanded by the application. Actually, one clear minimum requirement is that the device (channel, memory, teleportation system) cannot be thought of simply measuring out the quantum mechanical system, only to recreate later, or at a difference location a new quantum mechanical state based only on the classically transmitted/stored measurement result. These strategies are typically referred to as “intercept/resend” strategies.
We have been developing a tools box to exclude the intercept/resend strategies. Actually, quite often it is sufficient to test the device on just two different quantum states as input. One just has to measure the output state of the device with at least two non-commuting measurements. In many implementations, especially optical systems, the measurement results give only very little information about the overall state, for example first and second moments of optical quadrature variables. Still, even with this limited information we can often demonstrate that the device must have been operating in the full quantum domain! In a way, we work on the minimalistic set of experiments that can demonstrate quantum behaviour.
We demonstrated our method not only for single mode quantum devices, but also for two-mode devices. An important device that need to be tested is a quantum channel transmitting either polarization states or transmitting two sequential pulses. These channels are used for quantum key distribution and one needs to be sure that the signals and the measurements can exclude intercept/resend attacks in order to be able at all to distill secret key from the data.
[H. Häseler, J. Rigas, O. Gühne and N. Lütkenhaus, Verifying Entanglement in Quantum Optical Systems; pages 151-156, Proceedings of the QCMC2006, Ed. O.Hirota, J. H. Shapiro and M. Sasaki, NICT Press, 2007, ISBN978-4-904020-00-5 (6 pages)]
Proposed quantum benchmarking page
- Bell inequalities and nonlocality
We investigate links between local hidden variable theories and the implication of their existence in a quantum communication context.
- Measurement implementation via linear optics
In this line of work we investigate which kind of measurements can be implemented by linear optics and simple add-ons, such as auxiliary states, measurements, and classical feed-forward. In the first work, we were able to show that no exact implementation of the Bell-measurement on two qubits is possible, where the qubits are represented by single photons in the polarization degree of freedom. In subsequent work we showed that the optimum probability in a simple passive set-up is 50%. Later, we picked up again this line of work in a more general way, formulating a simple hierarchy of conditions for exact implementation of measurements by linear optics, so that by now the example of the Bell-state measurement becomes a back-of-the-envelope calculation. In the latest work in this series, we gave a framework to extend the results to general POVM measurements, as opposed to the restricted class of projective von Neumann measurements.