Hermann Kampermann

Networks of nodes connected by pairwise quantum key distribution (QKD) links are actively developing now. We consider the following problem: Given pairwise secret keys from QKD, how to agree on a common (conference) key for the whole network using classical communication? We propose an algorithm based on spanning tree packing from the graph theory and prove its optimality. The same algorithm can be applied for the GHZ distillation in pair-entangled networks.

The security of prepare-and-measure satellite-based quantum key distribution (QKD), under restricted eavesdropping scenarios, is addressed. We particularly consider cases where the eavesdropper, Eve, has limited access to the transmitted signal by Alice, and/or Bob’s receiver station. For instance, Eve can only receive an attenuated version of the transmitted signals. This results in settings where an uncharacterized bypass channel, inaccessible to Eve, can also carry signals to Bob. We obtain generic bounds on the key rate in the presence of bypass channels and apply them to continuous-variable QKD protocols with Gaussian encoding as well as to the family of BB84 protocols. We find regimes of operation in which the above restrictions on Eve can considerably improve system performance. Our work opens up new security frameworks for spaceborne quantum communications systems.

The characterization of quantum devices is crucial for their practical implementation but can be costly in experimental effort and classical post-processing. Therefore, it is desirable to measure only information that is relevant for specific applications and develop protocols that require little additional effort. In this work, we focus on the characterization of quantum computers in the context of stabilizer quantum error correction. We prove that (i) physical and (ii) logical error channels induced by Pauli noise can be estimated from syndrome data under minimal conditions. Essentially, any Pauli channel a code can correct can also be estimated from its syndrome measurements. We also provide a concrete estimation algorithm for this task.

We investigate the problem of conference key agreement in pair entangled networks (PEN) where the parties can share bipartite entangled states. In such networks, a source whose global state factorizes into bipartite “pair-entangled network” (PEN) states is distributed to honest parties which can perform local operations and public classical post-processing (LOSR+PP) to establish a shared secret key among each other. In this setting, we derive several new upper bounds on the achievable conference key rate. In particular for pure PEN states we show that the optimal key rate can be achieved by a bipartite QKD strategy.

We investigate the security of a quantum key distribution scheme, where Bob right after each detection announces publicly his choice of measurement basis, and the measurement results if the measurement is performed in the testing basis (used for parameter estimation). Such a scheme saves memory and communication time on both sides by not sending all the classical information only at the end of each block but immediately after each detection. We prove its security and show that this method will not reduce the key rate compared to conventional sifting.

When the outcomes of a set of parties measuring their local quantum systems exhibit non-local correlations by violating a Bell inequality, one can infer that such outcomes are secret to some extent. This is at the core of the security of many device-independent (DI) protocols, such as DI randomness expansion and DI conference key agreement. We quantify the amount of secret randomness in the parties’ outcomes by analytically computing their conditional von Neumann entropies as a function of the Bell violation, for different Bell inequalities.

Entanglement distribution between very distant parties allows several interesting quantum-enabled protocols to be performed, in the fields of quantum communication, metrology and distributed computation. However, achieving this task over global distances (thousands of km) is very daunting, due to the exponential losses of light in optical fibres. The concept of a quantum repeater has been introduced to counter this problem. Such a device allows, using quantum memories and protocols based on entanglement swapping or quantum error correction, to connect several elementary links and enlarge the achievable distance. An alternative solution is represented by satellite-relayed free-space channels, that have already been proven to be feasible with current technology. Using a double downlink from a single satellite, however, the maximum distance between the ground stations is limited to {1500-2000} km, due to the additional losses encountered at low elevation angles. Through quantum repeaters, few of these satellite links can be chained together to reach global distances. In this work we propose and study a scheme in which entanglement sources and quantum repeaters are placed on board of satellites, orbiting around the Earth in the string of pearls configuration. This allows to connect two users on the ground via free-space optical links outside the atmosphere, achieving far superior distance-to-loss ratio with respect to the standard fibre-based implementation. In this way, a small number of intermediate nodes is enough to achieve entanglement distribution over global distances at a reasonable rate. The performance of this repeater chain is assessed in terms of the secret key rate achievable by the BB-84 cryptographic protocol, taking into account the most important sources of noise. We perform a comparison with other repeater chain architectures and show that our scheme is superior in almost every situation, achieving higher key rates, reliability and flexibility. These results have been obtained assuming reasonably conservative values of the parameters of the setup, such as the size of the optical elements and the efficiency of the quantum memories. The feasibility of the implementation in the mid-term future is analysed, based on recent developments in space-borne technology. We finally discuss some exemplary orbital configurations to connect several pairs of cities around the world with very small satellite constellations and estimate the cost of such an infrastructure. The integration of satellite-based links with ground repeater networks can be envisaged to represent the backbone of the future Quantum Internet. C. Liorni, H. Kampermann, D. Bruß, arXiv:2005.10146, 2020

We consider a device-independent scenario where N parties test the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality. By exploiting the inequality’s symmetries, we drastically simplify the general form of the quantum state that can be considered, without loss of generality. We then derive an upper bound on the maximal violation of the MABK inequality attained by an arbitrary N-qubit state, as a function of the state’s parameters. The two results enable us to derive analytical bounds on the von Neumann entropy of the parties’ outcomes, conditioned on the eavesdropper’s information. These quantities are crucial for the security of many cryptographic protocols and better bounds lead to more robust protocols. In particular, we bound the conditional entropy of a single party’s outcome and the joint conditional entropy of two parties’ outcomes, as a function of the MABK violation observed by three parties. We extend the former bound to N parties and prove its tightness, while we observe that the latter significantly improves previous results.

We investigate quantum repeaters using quantum error correction codes (CSS codes) in the context of quantum key distribution. We show in which range of parameters it is useful to employ the conventional repeater scheme with distillation in comparison the quantum repeater using encoding. We found that using quantum repeater with quantum error correction codes we can decrease the restrictions on the gate errors for obtaining a non-zero secret key rate.