Duality of privacy amplification against quantum adversaries and data compression with quantum side information

We show that the tasks of privacy amplification against quantum adversaries and data compression with quantum side information are dual in the sense that the ability to perform one implies the ability to perform the other. These are two of the most important primitives in classical information theory, and are shown to be connected by complementarity and the uncertainty principle in the quantum setting. Applications include a new uncertainty principle formulated in terms of smooth min- and max-entropies, as well as new conditions for approximate quantum error correction.Comment: v2: Includes a derivation of an entropic uncertainty principle for smooth min- and max-entropies. Discussion of the Holevo-Schumacher-Westmoreland theorem remove

Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way post-processing

We derive a bound for the security of QKD with finite resources under one-way post-processing, based on a definition of security that is composable and has an operational meaning. While our proof relies on the assumption of collective attacks, unconditional security follows immediately for standard protocols like Bennett-Brassard 1984 and six-states. For single-qubit implementations of such protocols, we find that the secret key rate becomes positive when at least N\sim 10^5 signals are exchanged and processed. For any other discrete-variable protocol, unconditional security can be obtained using the exponential de Finetti theorem, but the additional overhead leads to very pessimistic estimates

Scanning Tunneling Spectroscopy of Bi2Sr2CuO6+d: New Evidence for the Common Origin of the Pseudogap and Superconductivity

Using scanning tunneling spectroscopy, we investigated the temperature dependence of the quasiparticle density of states of overdoped Bi2Sr2CuO6+δ between 275 mK and 82 K. Below Tc = 10 K, the spectra show a gap with well-defined coherence peaks at ±Δp≃12 meV, which disappear at Tc. Above Tc, the spectra display a clear pseudogap of the same magnitude, gradually filling up and vanishing at T*≃68 K. The comparison with Bi2Sr2CaCu2O8+δ demonstrates that the pseudogap and the superconducting gap scale with each other, providing strong evidence that they have a common origin

Device for in-situ cleaving of hard crystals

Cleaving crystals in a vacuum chamber is a simple method for obtaining atomically flat and clean surfaces for materials that have a preferential cleaving plane. Most in-situ cleavers use parallel cutting edges that are applied from two sides on the sample. We found in ambient experiments that diagonal cutting pliers, where the cleavage force is introduced in a single point instead of a line work very well also for hard materials. Here, we incorporate the diagonal cutting plier principle in a design compatible with ultra-high vacuum requirements. We show optical microscopy (mm scale) and atomic force microscopy (atomic scale) images of NiO(001) surfaces cleaved with this device.Comment: 7 pages, 3 figures Submitted to Review of Scientific Instruments (2005

Linear and field-independent relation between vortex core state energy and gap in Bi2Sr2CaCu2O8+d

We present a scanning tunneling spectroscopy study on quasiparticle states in vortex cores in Bi2Sr2CaCu2O8+δ. The energy of the observed vortex core states shows an approximately linear scaling with the superconducting gap in the region just outside the core. This clearly distinguishes them from conventional localized core states and is a signature of the mechanism responsible for their discrete appearance in high-temperature superconductors. The energy scaling of the vortex core states also suggests a common nature of vortex cores in Bi2Sr2CaCu2O8+δ and YBa2Cu3O7-δ. Finally, these states do not show any dependence on the applied magnetic field between 1 and 6 T

Device independent quantum key distribution secure against coherent attacks with memoryless measurement devices

Device independent quantum key distribution aims to provide a higher degree of security than traditional QKD schemes by reducing the number of assumptions that need to be made about the physical devices used. The previous proof of security by Pironio et al. applies only to collective attacks where the state is identical and independent and the measurement devices operate identically for each trial in the protocol. We extend this result to a more general class of attacks where the state is arbitrary and the measurement devices have no memory. We accomplish this by a reduction of arbitrary adversary strategies to qubit strategies and a proof of security for qubit strategies based on the previous proof by Pironio et al. and techniques adapted from Renner.Comment: 13 pages. Expanded main proofs with more detail, miscellaneous edits for clarit

A measure of majorisation emerging from single-shot statistical mechanics

The use of the von Neumann entropy in formulating the laws of thermodynamics has recently been challenged. It is associated with the average work whereas the work guaranteed to be extracted in any single run of an experiment is the more interesting quantity in general. We show that an expression that quantifies majorisation determines the optimal guaranteed work. We argue it should therefore be the central quantity of statistical mechanics, rather than the von Neumann entropy. In the limit of many identical and independent subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered but in the non-equilbrium regime the optimal guaranteed work can be radically different to the optimal average. Moreover our measure of majorisation governs which evolutions can be realized via thermal interactions, whereas the nondecrease of the von Neumann entropy is not sufficiently restrictive. Our results are inspired by single-shot information theory.Comment: 54 pages (15+39), 9 figures. Changed title / changed presentation, same main results / added minor result on pure bipartite state entanglement (appendix G) / near to published versio

Quantum circuit for security proof of quantum key distribution without encryption of error syndrome and noisy processing

One of the simplest security proofs of quantum key distribution is based on the so-called complementarity scenario, which involves the complementarity control of an actual protocol and a virtual protocol [M. Koashi, e-print arXiv:0704.3661 (2007)]. The existing virtual protocol has a limitation in classical postprocessing, i.e., the syndrome for the error-correction step has to be encrypted. In this paper, we remove this limitation by constructing a quantum circuit for the virtual protocol. Moreover, our circuit with a shield system gives an intuitive proof of why adding noise to the sifted key increases the bit error rate threshold in the general case in which one of the parties does not possess a qubit. Thus, our circuit bridges the simple proof and the use of wider classes of classical postprocessing.Comment: 8 pages, 2 figures. Typo correcte