09:20 to 10:10 Quantum and secret correlations Quantum and secret correlations are two valuable resources in Quantum Information Theory and Cryptography, respectively. They both have the property of being monogamous: the more two parties share secret or quantum correlations, the less they are coupled to the environment. The analogies between these two resources become more evident if one compares the usual quantum (secret) correlation manipulation scenario: N parties share a quantum state rho_A1AN (probability distribution P(A1,...,AN)) that is also entangled (correlated) to the environment (Eve). From an operational point of view, one would like to know 1) how many entangled bits (secret bits) are required for the preparation of the state (probability distribution) and 2) how many entangled bits (secret bits) can be extracted, or distilled, from the state (probability distribution). Exploiting these analogies, the following results can be proven: 1) All two-qubit entangled states allow a secure key distribution when Alice, Bob and Eve perform operations at the single-copy level. 2) The preparation of a probability distribution requires entanglement if and only if secret bits are consumed in an alternative preparation using only classical means. This implies that all the entangled states, independently of their distillability properties, can be mapped into probability distributions containing secret correlations. 3) There exists a cryptographic analog of bound entanglement, known as bound information. As it happens for bound entanglement, bound information can be activated: the mixture of non-distillable probability distributions can lead to a distillable one. INI 1 10:10 to 11:00 Decoy state quantum key distribution Quantum key distribution (QKD) allows two parties to communicate in absolute security based on the fundamental laws of physics. Up till now, it is widely believed that unconditionally secure QKD with the standard Bennett-Brassard (BB84) protocol is only possible at rather low key generation rate and short distances. Previously proposed methods (including single-photon sources) to extend the distances of BB84 and increase key generation rate are mostly experimental and present daunting experimental challenges. Here, we present a simple theoretical idea that will achieve these goals by using only current technology. Our method is to develop substantially the decoy state idea of Hwang and combine it with standard entanglement distillation approach to security proofs. Our results show that secure QKD is possible at a key generation rate as high as $O (\eta)$ (as opposed to $O(\eta^2)$ in prior art) where $\eta$ is the overall transmission probability of the channel and fiber-based QKD can be made unconditionally secure over 100km. In summary, we can have the best of both worlds---making the best use of our imperfect experimental apparatus and yet getting the strongest level of security--- unconditional security, which is the Holy Grail of quantum cryptography. Our method is, therefore, a significant step in bridging the big gap between the theory and practice of QKD. INI 1 11:30 to 12:20 N Gisin ([Geneva])Simulation of singlet correlation without any communication, but using a weaker resource: a "non-local machine" The importance of quantum entanglement is by now widely appreciated as a resource for quantum information applications. A unit of entanglement has been identifies and named e-bit; it consists of a pair of maximally entangled qubits, e.g. of a singlet: the same singlet that Bohm used in his version of the EPR paradox. A few years ago connection with communication complexity started to be studied, with question like how much communication is required to simulate an e-bit? From Bell inequality we know that it is impossible to simulate a singlet without any communication even if one assumes that both parties share local hidden variables, or in modern terminology, share randomness. Recently, Tonner and Bacon proved that actually a single bit of communication suffice for perfect simulation. Independently from the above story, Popescu and Rochlich raised the following question: can there be correlation stronger than the quantum mechanical ones that do not allow one to signal? They answered by showing a hypothetical non-local machine that does not allow signaling, yet violates the CHSH-bell inequality by the absolute maximal value of 4 (while quantum correlation achieve at most $2\sqrt{2}$. They concluded asking why Nature is non-local, but not maximally non-local, where the maximum would be only limited by the no-signaling constraint? It is straightforward to simulate the PR machine with a single bit of communication. Consequently, the PR nonlocal machine is a strictly weaker resource than a bit of communication. We show that singlets can be simulated using only one instance of the PR non-local machine. Hence, assuming that Nature is sparing with resources, one is be tempted to conclude that she is using something like the non-local machine. Finally, we raise the question whether correlations arising from partially entangled qubits can be simulated using only an e-bit? INI 1 14:00 to 14:50 A Kent ([Cambridge])Remarks on mistrustful quantum and relativistic cryptography I review some ideas on what cryptographic tasks might or might not be implementable with security guaranteed by special relativity and/or quantum theory. INI 1 15:30 to 16:20 Provably secure experimental quantum bit string generation Coin Tossing is the problem in which two parties who do not trust each other want to generate a random coin. Quantum communication allows the parties to generate a coin with bias less than ½, which is impossible classically. However even quantum communication cannot guarantee that the bits are perfectly random. Bit string generation is the generalisation of coin tossing when the two parties want to generate a large number n of coins. We discuss the theory of quantum bit string generation and show that much better security is possible than for quantum coin tossing. We also report on an experiment in which a string of bits is generated which more random than is possible classically. INI 1 16:20 to 17:10 A new inequality for the von Neuman entropy Strong subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. I will describe some work with Andreas Winter in which we prove a new inequality for the von Neumann entropy which is independent of strong subadditivity. This work sheds light on extremal types of entanglement for multi-party quantum states. INI 1