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

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

The work value of information

We present quantitative relations between work and information that are valid both for finite sized and internally correlated systems as well in the thermodynamical limit. We suggest work extraction should be viewed as a game where the amount of work an agent can extract depends on how well it can guess the micro-state of the system. In general it depends both on the agent's knowledge and risk-tolerance, because the agent can bet on facts that are not certain and thereby risk failure of the work extraction. We derive strikingly simple expressions for the extractable work in the extreme cases of effectively zero- and arbitrary risk tolerance respectively, thereby enveloping all cases. Our derivation makes a connection between heat engines and the smooth entropy approach. The latter has recently extended Shannon theory to encompass finite sized and internally correlated bit strings, and our analysis points the way to an analogous extension of statistical mechanics.Comment: 5 pages, 4 figure

Locking classical information

It is known that the maximum classical mutual information that can be achieved between measurements on a pair of quantum systems can drastically underestimate the quantum mutual information between those systems. In this article, we quantify this distinction between classical and quantum information by demonstrating that after removing a logarithmic-sized quantum system from one half of a pair of perfectly correlated bitstrings, even the most sensitive pair of measurements might only yield outcomes essentially independent of each other. This effect is a form of information locking but the definition we use is strictly stronger than those used previously. Moreover, we find that this property is generic, in the sense that it occurs when removing a random subsystem. As such, the effect might be relevant to statistical mechanics or black hole physics. Previous work on information locking had always assumed a uniform message. In this article, we assume only a min-entropy bound on the message and also explore the effect of entanglement. We find that classical information is strongly locked almost until it can be completely decoded. As a cryptographic application of these results, we exhibit a quantum key distribution protocol that is "secure" if the eavesdropper's information about the secret key is measured using the accessible information but in which leakage of even a logarithmic number of key bits compromises the secrecy of all the others.Comment: 32 pages, 2 figure

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

An Assessment of African Union Security Architecture in the Management of Conflicts in Africa: Case Study of Somalia

Africa is one of the most vulnerable continents in the world due to social dislocation, international politics and compelling internal contradictions. Research shows that towards the close of 1966, almost half of the war-related deaths in the world were located in Africa accounting for over 8 million of the 22 million refugees across the globe. The Rwanda genocide claim over 800,000 deaths in 1994, over 4.5million death occurred in the last decade of the 20th century in other conflict zone in Africa such as Democratic Republic of the Congo, Sudan, Nigeria, Liberia, Ethiopia, Angola, Mozambique, Uganda etc. this work interrogate the AU security architecture APSA in the management of Africa conflicts. APSA is the collective term for a number of specific capability areas intended to strengthen Africa’s ability to respond to the peace and security challenges facing the continent. The work uses the Somalia conflict as a case in study. It identifies the strengths and weaknesses of APSA however, it concludes that APSA perfumed creditably well in Somalia but call for deeper commitment by member states to the cause of Africa development and integration. Keywords: APSA. Conflict, peace keeping, peace enforcement, Protocol, AMISO

On the universality of small scale turbulence

The proposed universality of small scale turbulence is investigated for a set of measurements in a cryogenic free jet with a variation of the Reynolds number (Re) from 8500 to 10^6. The traditional analysis of the statistics of velocity increments by means of structure functions or probability density functions is replaced by a new method which is based on the theory of stochastic Markovian processes. It gives access to a more complete characterization by means of joint probabilities of finding velocity increments at several scales. Based on this more precise method our results call in question the concept of universality.Comment: 4 pages, 4 figure

The fabrication of reproducible superconducting scanning tunneling microscope tips

Superconducting scanning tunneling microscope tips have been fabricated with a high degree of reproducibility. The fabrication process relies on sequential deposition of superconducting Pb and a proximity-coupled Ag capping layer onto a Pt/Ir tip. The tips were characterized by tunneling into both normal-metal and superconducting films. The simplicity of the fabrication process, along with the stability and reproducibility of the tips, clear the way for tunneling studies with a well-characterized, scannable superconducting electrode.Comment: 4 pages, 3 figures, REVTeX. Submitted to Rev. Sci. Instru

Asymptotic Entanglement Dynamics and Geometry of Quantum States

A given dynamics for a composite quantum system can exhibit several distinct properties for the asymptotic entanglement behavior, like entanglement sudden death, asymptotic death of entanglement, sudden birth of entanglement, etc. A classification of the possible situations was given in [M. O. Terra Cunha, {\emph{New J. Phys}} {\bf{9}}, 237 (2007)] but for some classes there were no known examples. In this work we give a better classification for the possibile relaxing dynamics at the light of the geometry of their set of asymptotic states and give explicit examples for all the classes. Although the classification is completely general, in the search of examples it is sufficient to use two qubits with dynamics given by differential equations in Lindblad form (some of them non-autonomous). We also investigate, in each case, the probabilities to find each possible behavior for random initial states.Comment: 9 pages, 2 figures; revised version accepted for publication in J. Phys. A: Math. Theo

The Uncertainty Principle in the Presence of Quantum Memory

The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements, such as position and momentum, on a particle. It implies that one cannot predict the outcomes for both possible choices of measurement to arbitrary precision, even if information about the preparation of the particle is available in a classical memory. However, if the particle is prepared entangled with a quantum memory, a device which is likely to soon be available, it is possible to predict the outcomes for both measurement choices precisely. In this work we strengthen the uncertainty principle to incorporate this case, providing a lower bound on the uncertainties which depends on the amount of entanglement between the particle and the quantum memory. We detail the application of our result to witnessing entanglement and to quantum key distribution.Comment: 5 pages plus 12 of supplementary information. Updated to match the journal versio