Quantum Bit Commitment with a Composite Evidence

Entanglement-based attacks, which are subtle and powerful, are usually believed to render quantum bit commitment insecure. We point out that the no-go argument leading to this view implicitly assumes the evidence-of-commitment to be a monolithic quantum system. We argue that more general evidence structures, allowing for a composite, hybrid (classical-quantum) evidence, conduce to improved security. In particular, we present and prove the security of the following protocol: Bob sends Alice an anonymous state. She inscribes her commitment $b$ by measuring part of it in the + (for $b = 0$) or $\times$ (for $b=1$) basis. She then communicates to him the (classical) measurement outcome $R_x$ and the part-measured anonymous state interpolated into other, randomly prepared qubits as her evidence-of-commitment.Comment: 6 pages, minor changes, journal reference adde

Thermal and mechanical structure of the upper mantle: A comparison between continental and oceanic models

Temperature, velocity, and viscosity profiles for coupled thermal and mechanical models of the upper mantle beneath continental shields and old ocean basins show that under the continents, both tectonic plates and the asthenosphere, are thicker than they are beneath the oceans. The minimum value of viscosity in the continental asthenosphere is about an order of magnitude larger than in the shear zone beneath oceans. The shear stress or drag underneath continental plates is also approximately an order of magnitude larger than the drag on oceanic plates. Effects of shear heating may account for flattening of ocean floor topography and heat flux in old ocean basins

Oceanic lithosphere and asthenosphere: The thermal and mechanical structure

A coupled thermal and mechanical solid state model of the oceanic lithosphere and asthenosphere is presented. The model includes vertical conduction of heat with a temperature dependent thermal conductivity, horizontal and vertical advection of heat, viscous dissipation or shear heating, and linear or nonlinear deformation mechanisms with temperature and pressure dependent constitutive relations between shear stress and strain rate. A constant horizontal velocity u sub 0 and temperature t sub 0 at the surface and zero horizontal velocity and constant temperature t sub infinity at great depth are required. In addition to numerical values of the thermal and mechanical properties of the medium, only the values of u sub 0, t sub 0 and t sub infinity are specified. The model determines the depth and age dependent temperature horizontal and vertical velocity, and viscosity structures of the lithosphere and asthenosphere. In particular, ocean floor topography, oceanic heat flow, and lithosphere thickness are deduced as functions of the age of the ocean floor

Statistical Geometry in Quantum Mechanics

A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of probability distributions into the Hilbert space H. By consideration of the square-root density function we can regard M as a submanifold of the unit sphere in H. Therefore, H embodies the `state space' of the probability distributions, and the geometry of M can be described in terms of the embedding of in H. The geometry in question is characterised by a natural Riemannian metric (the Fisher-Rao metric), thus allowing us to formulate the principles of classical statistical inference in a natural geometric setting. In particular, we focus attention on the variance lower bounds for statistical estimation, and establish generalisations of the classical Cramer-Rao and Bhattacharyya inequalities. The statistical model M is then specialised to the case of a submanifold of the state space of a quantum mechanical system. This is pursued by introducing a compatible complex structure on the underlying real Hilbert space, which allows the operations of ordinary quantum mechanics to be reinterpreted in the language of real Hilbert space geometry. The application of generalised variance bounds in the case of quantum statistical estimation leads to a set of higher order corrections to the Heisenberg uncertainty relations for canonically conjugate observables.Comment: 32 pages, LaTex file, Extended version to include quantum measurement theor

Minimum-error discrimination between mixed quantum states

We derive a general lower bound on the minimum-error probability for {\it ambiguous discrimination} between arbitrary $m$ mixed quantum states with given prior probabilities. When $m=2$, this bound is precisely the well-known Helstrom limit. Also, we give a general lower bound on the minimum-error probability for discriminating quantum operations. Then we further analyze how this lower bound is attainable for ambiguous discrimination of mixed quantum states by presenting necessary and sufficient conditions related to it. Furthermore, with a restricted condition, we work out a upper bound on the minimum-error probability for ambiguous discrimination of mixed quantum states. Therefore, some sufficient conditions are obtained for the minimum-error probability attaining this bound. Finally, under the condition of the minimum-error probability attaining this bound, we compare the minimum-error probability for {\it ambiguously} discriminating arbitrary $m$ mixed quantum states with the optimal failure probability for {\it unambiguously} discriminating the same states.Comment: A further revised version, and some results have been adde

Quantum-state filtering applied to the discrimination of Boolean functions

Quantum state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs.The simplest case, when the N given states are divided into two subsets and the first set consists of one state only while the second consists of all of the remaining states, is termed quantum state filtering. We derived previously the optimal strategy for the case of N non-orthogonal states, {|\psi_{1} >, ..., |\psi_{N} >}, for distinguishing |\psi_1 > from the set {|\psi_2 >, ..., |\psi_N >} and the corresponding optimal success and failure probabilities. In a previous paper [PRL 90, 257901 (2003)], we sketched an appplication of the results to probabilistic quantum algorithms. Here we fill in the gaps and give the complete derivation of the probabilstic quantum algorithm that can optimally distinguish between two classes of Boolean functions, that of the balanced functions and that of the biased functions. The algorithm is probabilistic, it fails sometimes but when it does it lets us know that it did. Our approach can be considered as a generalization of the Deutsch-Jozsa algorithm that was developed for the discrimination of balanced and constant Boolean functions.Comment: 8 page

High temperature cavity polaritons in epitaxial Er_2O_3 on silicon

Cavity polaritons around two Er^(3+) optical transitions are observed in microdisk resonators fabricated from epitaxial Er_2O_3 on Si(111). Using a pump-probe method, spectral anticrossings and linewidth averaging of the polariton modes are measured in the cavity transmission and luminescence at temperatures above 361 K

Helstrom Theorem by No-Signaling Condition

We prove a special case of Helstrom theorem by using no-signaling condition in the special theory of relativity that faster-than-light communication is impossible.Comment: Minor corrections (A reference added, discussion part deleted, typos in equations corrected), 2 pages, RevTe

Plexcitons: Dirac points and topological modes

Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. We consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional bandstructure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. These Dirac cones may open up in energy by simultaneously interfacing the metal with a magneto-optical layer and subjecting the whole system to a perpendicular magnetic field. The resulting energy gap becomes populated with topologically protected one-way modes which travel at the interface of this plexcitonic system. Our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter as well as of novel ways to direct energy flow at the nanoscale