Enabling Data-Driven Transportation Safety Improvements in Rural Alaska

Safety improvements require funding. A clear need must be demonstrated to secure funding. For transportation safety, data, especially data about past crashes, is the usual method of demonstrating need. However, in rural locations, such data is often not available, or is not in a form amenable to use in funding applications. This research aids rural entities, often federally recognized tribes and small villages acquire data needed for funding applications. Two aspects of work product are the development of a traffic counting application for an iPad or similar device, and a review of the data requirements of the major transportation funding agencies. The traffic-counting app, UAF Traffic, demonstrated its ability to count traffic and turning movements for cars and trucks, as well as ATVs, snow machines, pedestrians, bicycles, and dog sleds. The review of the major agencies demonstrated that all the likely funders would accept qualitative data and Road Safety Audits. However, quantitative data, if it was available, was helpful

Recovery of entanglement lost in entanglement manipulation

When an entangled state is transformed into another one with probability one by local operations and classical communication, the quantity of entanglement decreases. This letter shows that entanglement lost in the manipulation can be partially recovered by an auxiliary entangled pair. As an application, a maximally entangled pair can be obtained from two partially entangled pairs with probability one. Finally, this recovery scheme reveals a fundamental property of entanglement relevant to the existence of incomparable states.Comment: 4 pages, 2 figures, REVTeX; minor correction

Entanglement Swapping Chains for General Pure States

We consider entanglement swapping schemes with general (rather than maximally) entangled bipartite states of arbitary dimension shared pairwise between three or more parties in a chain. The intermediate parties perform generalised Bell measurements with the result that the two end parties end up sharing a entangled state which can be converted into maximally entangled states. We obtain an expression for the average amount of maximal entanglement concentrated in such a scheme and show that in a certain reasonably broad class of cases this scheme is provably optimal and that, in these cases, the amount of entanglement concentrated between the two ends is equal to that which could be concentrated from the weakest link in the chain.Comment: 18 pages, 5 figure

The trumping relation and the structure of the bipartite entangled states

The majorization relation has been shown to be useful in classifying which transformations of jointly held quantum states are possible using local operations and classical communication. In some cases, a direct transformation between two states is not possible, but it becomes possible in the presence of another state (known as a catalyst); this situation is described mathematically by the trumping relation, an extension of majorization. The structure of the trumping relation is not nearly as well understood as that of majorization. We give an introduction to this subject and derive some new results. Most notably, we show that the dimension of the required catalyst is in general unbounded; there is no integer $k$ such that it suffices to consider catalysts of dimension $k$ or less in determining which states can be catalyzed into a given state. We also show that almost all bipartite entangled states are potentially useful as catalysts.Comment: 7 pages, RevTe

Countering Quantum Noise with Supplementary Classical Information

We consider situations in which i) Alice wishes to send quantum information to Bob via a noisy quantum channel, ii) Alice has a classical description of the states she wishes to send and iii) Alice can make use of a finite amount of noiseless classical information. After setting up the problem in general, we focus attention on one specific scenario in which Alice sends a known qubit down a depolarizing channel along with a noiseless cbit. We describe a protocol which we conjecture is optimal and calculate the average fidelity obtained. A surprising amount of structure is revealed even for this simple case which suggests that relationships between quantum and classical information could in general be very intricate.Comment: RevTeX, 5 pages, 2 figures Typo in reference 9 correcte

Parametrization and distillability of three-qubit entanglement

There is an ongoing effort to quantify entanglement of quantum pure states for systems with more than two subsystems. We consider three approaches to this problem for three-qubit states: choosing a basis which puts the state into a standard form, enumerating ``local invariants,'' and using operational quantities such as the number of maximally entangled states which can be distilled. In this paper we evaluate a particular standard form, the {\it Schmidt form}, which is a generalization of the Schmidt decomposition for bipartite pure states. We show how the coefficients in this case can be parametrized in terms of five physically meaningful local invariants; we use this form to prove the efficacy of a particular distillation technique for GHZ triplets; and we relate the yield of GHZs to classes of states with unusual entanglement properties, showing that these states represent extremes of distillability as functions of two local invariants.Comment: 17 pages RevTeX 3.0 including 2 figures (encapsulated Postscript) Final version, to appear in Physics Letters

The quantum one-time pad in the presence of an eavesdropper

A classical one-time pad allows two parties to send private messages over a public classical channel -- an eavesdropper who intercepts the communication learns nothing about the message. A quantum one-time pad is a shared quantum state which allows two parties to send private messages or private quantum states over a public quantum channel. If the eavesdropper intercepts the quantum communication she learns nothing about the message. In the classical case, a one-time pad can be created using shared and partially private correlations. Here we consider the quantum case in the presence of an eavesdropper, and find the single letter formula for the rate at which the two parties can send messages using a quantum one-time pad

A classical analogue of entanglement

We show that quantum entanglement has a very close classical analogue, namely secret classical correlations. The fundamental analogy stems from the behavior of quantum entanglement under local operations and classical communication and the behavior of secret correlations under local operations and public communication. A large number of derived analogies follow. In particular teleportation is analogous to the one-time-pad, the concept of ``pure state'' exists in the classical domain, entanglement concentration and dilution are essentially classical secrecy protocols, and single copy entanglement manipulations have such a close classical analog that the majorization results are reproduced in the classical setting. This analogy allows one to import questions from the quantum domain into the classical one, and vice-versa, helping to get a better understanding of both. Also, by identifying classical aspects of quantum entanglement it allows one to identify those aspects of entanglement which are uniquely quantum mechanical.Comment: 13 pages, references update