Sums of two s{s}-units via frey-hellegouarch curves

In this paper, we develop a new method for finding all perfect powers which can be expressed as the sum of two rational S-units, where S is a finite set of primes. Our approach is based upon the modularity of Galois representations and, for the most part, does not require lower bounds for linear forms in logarithms. Its main virtue is that it enables to carry out such a program explicitly, at least for certain small sets of primes S; we do so for S = {2, 3} and S = {3, 5, 7}.Comment: Missing solution in Prop. 5.4 added. To appear in Mathematics of Computatio

Security of continuous-variable quantum key distribution against general attacks

We prove the security of Gaussian continuous-variable quantum key distribution against arbitrary attacks in the finite-size regime. The novelty of our proof is to consider symmetries of quantum key distribution in phase space in order to show that, to good approximation, the Hilbert space of interest can be considered to be finite-dimensional, thereby allowing for the use of the postselection technique introduced by Christandl, Koenig and Renner (Phys. Rev. Lett. 102, 020504 (2009)). Our result greatly improves on previous work based on the de Finetti theorem which could not provide security for realistic, finite-size, implementations.Comment: 5 pages, plus 11 page appendi

Quantum Information Theory of Entanglement and Measurement

We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the description of quantum ensembles. We find that quantum conditional entropies can be negative for entangled systems, which leads to a violation of well-known bounds in Shannon information theory. Such a unified information-theoretic description of classical correlation and quantum entanglement clarifies the link between them: the latter can be viewed as ``super-correlation'' which can induce classical correlation when considering a tripartite or larger system. Furthermore, negative entropy and the associated clarification of entanglement paves the way to a natural information-theoretic description of the measurement process. This model, while unitary and causal, implies the well-known probabilistic results of conventional quantum mechanics. It also results in a simple interpretation of the Kholevo theorem limiting the accessible information in a quantum measurement.Comment: 26 pages with 6 figures. Expanded version of PhysComp'96 contributio

From Bell's Theorem to Secure Quantum Key Distribution

Any Quantum Key Distribution (QKD) protocol consists first of sequences of measurements that produce some correlation between classical data. We show that these correlation data must violate some Bell inequality in order to contain distillable secrecy, if not they could be produced by quantum measurements performed on a separable state of larger dimension. We introduce a new QKD protocol and prove its security against any individual attack by an adversary only limited by the no-signaling condition.Comment: 5 pages, 2 figures, REVTEX

The virtual photon approximation for three-body interatomic Coulombic decay

Interatomic Coulombic decay (ICD) is a mechanism which allows microscopic objects to rapidly exchange energy. When the two objects are distant, the energy transfer between the donor and acceptor species takes place via the exchange of a virtual photon. On the contrary, recent ab initio calculations have revealed that the presence of a third passive species can significantly enhance the ICD rate at short distances due to the effects of electronic wave function overlap and charge transfer states [Phys. Rev. Lett. 119, 083403 (2017)]. Here, we develop a virtual photon description of three-body ICD, showing that a mediator atom can have a significant influence at much larger distances. In this regime, this impact is due to the scattering of virtual photons off the mediator, allowing for simple analytical results and being manifest in a distinct geometry-dependence which includes interference effects. As a striking example, we show that in the retarded regime ICD can be substantially enhanced or suppressed depending on the position of the ICD-inactive object, even if the latter is far from both donor and acceptor species

Quantum bit commitment under Gaussian constraints

Quantum bit commitment has long been known to be impossible. Nevertheless, just as in the classical case, imposing certain constraints on the power of the parties may enable the construction of asymptotically secure protocols. Here, we introduce a quantum bit commitment protocol and prove that it is asymptotically secure if cheating is restricted to Gaussian operations. This protocol exploits continuous-variable quantum optical carriers, for which such a Gaussian constraint is experimentally relevant as the high optical nonlinearity needed to effect deterministic non-Gaussian cheating is inaccessible.Comment: 9 pages, 6 figure

Quantum correlations and secret bits

It is shown that (i) all entangled states can be mapped by single-copy measurements into probability distributions containing secret correlations, and (ii) if a probability distribution obtained from a quantum state contains secret correlations, then this state has to be entangled. These results prove the existence of a two-way connection between secret and quantum correlations in the process of preparation. They also imply that either it is possible to map any bound entangled state into a distillable probability distribution or bipartite bound information exists.Comment: 4 pages, published versio

Economical quantum cloning in any dimension

The possibility of cloning a d-dimensional quantum system without an ancilla is explored, extending on the economical phase-covariant cloning machine found in [Phys. Rev. A {\bf 60}, 2764 (1999)] for qubits. We prove the impossibility of constructing an economical version of the optimal universal cloning machine in any dimension. We also show, using an ansatz on the generic form of cloning machines, that the d-dimensional phase-covariant cloner, which optimally clones all uniform superpositions, can be realized economically only in dimension d=2. The used ansatz is supported by numerical evidence up to d=7. An economical phase-covariant cloner can nevertheless be constructed for d>2, albeit with a lower fidelity than that of the optimal cloner requiring an ancilla. Finally, using again an ansatz on cloning machines, we show that an economical version of the Fourier-covariant cloner, which optimally clones the computational basis and its Fourier transform, is also possible only in dimension d=2.Comment: 8 pages RevTe

Automating drone image processing to map coral reef substrates using Google Earth Engine

While coral reef ecosystems hold immense biological, ecological, and economic value, frequent anthropogenic and environmental disturbances have caused these ecosystems to decline globally. Current coral reef monitoring methods include in situ surveys and analyzing remotely sensed data from satellites. However, in situ methods are often expensive and inconsistent in terms of time and space. High-resolution satellite imagery can also be expensive to acquire and subject to environmental conditions that conceal target features. High-resolution imagery gathered from remotely piloted aircraft systems (RPAS or drones) is an inexpensive alternative; however, processing drone imagery for analysis is time-consuming and complex. This study presents the first semi-automatic workflow for drone image processing with Google Earth Engine (GEE) and free and open source software (FOSS). With this workflow, we processed 230 drone images of Heron Reef, Australia and classified coral, sand, and rock/dead coral substrates with the Random Forest classifier. Our classification achieved an overall accuracy of 86% and mapped live coral cover with 92% accuracy. The presented methods enable efficient processing of drone imagery of any environment and can be useful when processing drone imagery for calibrating and validating satellite imagery