Stronger Attacks on Causality-Based Key Agreement

Remarkably, it has been shown that in principle, security proofs for quantum key-distribution (QKD) protocols can be independent of assumptions on the devices used and even of the fact that the adversary is limited by quantum theory. All that is required instead is the absence of any hidden information flow between the laboratories, a condition that can be enforced either by shielding or by space-time causality. All known schemes for such Causal Key Distribution (CKD) that offer noise-tolerance (and, hence, must use privacy amplification as a crucial step) require multiple devices carrying out measurements in parallel on each end of the protocol, where the number of devices grows with the desired level of security. We investigate the power of the adversary for more practical schemes, where both parties each use a single device carrying out measurements consecutively. We provide a novel construction of attacks that is strictly more powerful than the best known attacks and has the potential to decide the question whether such practical CKD schemes are possible in the negative

Distillation of Multi-Party Non-Locality With and Without Partial Communication

Non-local correlations are one of the most fascinating consequences of quantum physics from the point of view of information: Such correlations, although not allowing for signaling, are unexplainable by pre-shared information. The correlations have applications in cryptography, communication complexity, and sit at the very heart of many attempts of understanding quantum theory -- and its limits -- better in terms of classical information. In these contexts, the question is crucial whether such correlations can be distilled, i.e., whether weak correlations can be used for generating (a smaller amount of) stronger. Whereas the question has been studied quite extensively for bipartite correlations (yielding both pessimistic and optimistic results), only little is known in the multi-partite case. We show that a natural generalization of the well-known Popsecu-Rohrlich box can be distilled, by an adaptive protocol, to the algebraic maximum. We use this result further to show that a much bigger class of correlations, including all purely three-partite correlations, can be distilled from arbitrarily weak to maximal strength with partial communication, i.e., using only a subset of the channels required for the creation of the same correlation from scratch. In other words, we show that arbitrarily weak non-local correlations can have a "communication value" in the context of the generation of maximal non-locality.Comment: 5 pages, 3 figure

Lower bounds on the communication complexity of two-party (quantum) processes

The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the minimum of a convex functional over a space of suitable probability distributions. It is now proved that this optimization problem is the dual of a geometric programming maximization problem, which displays some appealing properties. First, the number of variables grows linearly with the input size. Second, the objective function is linear in the input parameters and the variables. Finally, the constraints do not depend on the input parameters. These properties imply that, once a feasible point is found, the computation of a lower bound on the communication cost in any two-party process is linearly complex. The studied scenario goes beyond quantum processes and includes the communication complexity scenario introduced by Yao. We illustrate the method by analytically deriving some non-trivial lower bounds. Finally, we conjecture the lower bound $n 2^n$ for a noiseless quantum channel with capacity $n$ qubits. This bound can have an interesting consequence in the context of the recent quantum-foundational debate on the reality of the quantum state.Comment: Conference version. A more extensive version with more details will be available soo