Improved Quantum Communication Complexity Bounds for Disjointness and Equality

We prove new bounds on the quantum communication complexity of the disjointness and equality problems. For the case of exact and non-deterministic protocols we show that these complexities are all equal to n+1, the previous best lower bound being n/2. We show this by improving a general bound for non-deterministic protocols of de Wolf. We also give an O(sqrt{n}c^{log^* n})-qubit bounded-error protocol for disjointness, modifying and improving the earlier O(sqrt{n}log n) protocol of Buhrman, Cleve, and Wigderson, and prove an Omega(sqrt{n}) lower bound for a large class of protocols that includes the BCW-protocol as well as our new protocol.Comment: 11 pages LaTe

A Method of Areas for Manipulating the Entanglement Properties of One Copy of a Two-Particle Pure State

We consider the problem of how to manipulate the entanglement properties of a general two-particle pure state, shared between Alice and Bob, by using only local operations at each end and classical communication between Alice and Bob. A method is developed in which this type of problem is found to be equivalent to a problem involving the cutting and pasting of certain shapes along with a certain colouring problem. We consider two problems. Firstly we find the most general way of manipulating the state to obtain maximally entangled states. After such a manipulation the entangled state |11>+|22>+....|mm> is obtained with probability p_m. We obtain an expression for the optimal average entanglement. Also, some results of Lo and Popescu pertaining to this problem are given simple geometric proofs. Secondly, we consider how to manipulate one two particle entangled pure state to another with certainty. We derive Nielsen's theorem (which states the necessary and sufficient condition for this to be possible) using the method of areas.Comment: 29 pages, 9 figures. Section 2.4 clarified. Error in second colouring theorem (section 3.2) corrected. Some other minor change

CONJOINT ANALYSIS OF GROUNDWATER PROTECTION PROGRAMS

Three conjoint models-a traditional ratings model, a ratings difference specification, and a binary response model-were used to value groundwater protection program alternatives. The last, which is virtually identical to a dichotomous choice contingent valuation specification, produced the smallest value estimates. This suggests that the conjoint model is very sensitive to model specifications and that traditional conjoint models may overestimate economic value because many respondents are not in the market for the commodity being valued.Resource /Energy Economics and Policy,

Causality and Cirel'son bounds

An EPR-Bell type experiment carried out on an entangled quantum system can produce correlations stronger than allowed by local realistic theories. However there are correlations that are no-signaling and are more non local than the quantum correlations. Here we show that any correlations more non local than those achievable in an EPR-Bell type experiment necessarily allow -in the context of the quantum formalism- both for signaling and for generation of entanglement. We use our approach to rederive Cirel'son bound for the CHSH expression, and we derive a new Cirel'son type bound for qutrits. We discuss in detail the interpretation of our approach.Comment: 5 page

Fast quantum algorithm for numerical gradient estimation

Given a blackbox for f, a smooth real scalar function of d real variables, one wants to estimate the gradient of f at a given point with n bits of precision. On a classical computer this requires a minimum of d+1 blackbox queries, whereas on a quantum computer it requires only one query regardless of d. The number of bits of precision to which f must be evaluated matches the classical requirement in the limit of large n.Comment: additional references and minor clarifications and corrections to version

Substituting a qubit for an arbitrarily large number of classical bits

We show that a qubit can be used to substitute for an arbitrarily large number of classical bits. We consider a physical system S interacting locally with a classical field phi(x) as it travels directly from point A to point B. The field has the property that its integrated value is an integer multiple of some constant. The problem is to determine whether the integer is odd or even. This task can be performed perfectly if S is a qubit. On the otherhand, if S is a classical system then we show that it must carry an arbitrarily large amount of classical information. We identify the physical reason for such a huge quantum advantage, and show that it also implies a large difference between the size of quantum and classical memories necessary for some computations. We also present a simple proof that no finite amount of one-way classical communication can perfectly simulate the effect of quantum entanglement.Comment: 8 pages, LaTeX, no figures. v2: added result on entanglement simulation with classical communication; v3: minor correction to main proof, change of title, added referenc

Quantum diagonalization of Hermitean matrices

To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource: Hermitean (N ×N) matrices can be diagonalized, in principle, by performing appropriate quantum mechanical measurements. To do so, one considers the given matrix as an observable of a single spin with appropriate length s which can be measured using a generalized Stern-Gerlach apparatus. Then, each run provides one eigenvalue of the observable. As the underlying working principle is the `collapse of the wavefunction' associated with a measurement, the procedure is neither a digital nor an analogue calculation - it defines thus a new example of a quantum mechanical method of computation

Universal quantum computation by discontinuous quantum walk

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantum computation in which a quantum walker takes discrete steps of continuous evolution. This `discontinuous' quantum walk employs perfect quantum state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, thereby ensuring unitary evolution without requiring the introduction of an ancillary coin space. The run time is linear in the number of simulated qubits and gates. The scheme allows multiple runs of the algorithm to be executed almost simultaneously by starting walkers one timestep apart.Comment: 7 pages, revte

Proceedings of a Summer Institute in Water Resources: Volume 1 - Philosophical, Institutional, and Legal Aspects of Water Resources

Foreward: Recognizing the need for training of individuals to meet the rapidly rising problems connected with water resources development, Utah State University, with National Science Foundation support, organized a Summer Institute in Water Resources for college teachers. it was hoped that participants carefully selected from all regions of the country would receive additional insight and stimulation to improve and enlarge water resources training programs at their own institutions. Thus, the accelerated dissemination of such knowledge on a national scale could be facilitated. Realizing further that the key to a successful institute of this nature lay in the excellence of its staff, efforts were made to obtain instructors with intimate knowledge and broad experience int he subject matter area they were asked to rpesent. In nearly every case those selected willingly accepted the invitation to participate, although this meant considerable monetary sacrifice and major adjustment of busy schedules. The subject matter treated paralleled regular offerings listed in the University catalog and is considered to be central or core to a water resources planning and management training program. one course treated the philosophical, historical, institutional, political, and legal aspects of water development. The responsibility for this course was shared jointly with Cleve H. Milligan, Charles E. Corker, and Wayne D. Criddle. The second course considered the principles of water resources economics and was presented by B. Delworth Gardner. The third course dealt with concepts of water quality management and was under the direction of P. H. McGauhey. The final course was on principles and procedures of regional resources planning and was presented jointly by Aaron Wiener, W. R. Derrick Sewell, and Harvey O. Banks. Having assembled a distinguished and diversified staff to present some of the best current professional thinking in the topics suggested in the preceding paragraph, it was felt most appropriate to attempt to put their lectures into writing. A proceedings of the Institute would have considerable utility beyong the Institute itself. Hence, the instructors were encouraged to prepare written material for the proceedings and were given secretarial and other assistance to aid them. This material has been organized according to the four major courses and is issued in four comanion volumes. Clearly, this has been a prodigious effort which required Institute staff and others to go the extra mile. Special thanks and recognition are due Mrs. Dorothy Riley who not only typed the entire proceedings but also attended to many details necessary for the successfult operations of the Institute. Jay M. Bagley served as director of the Institute and assumed a general coordinating and editing role in the development of these proceedings

Water Yields in Utah Developing a State Water Plan

Need and Importance of Study Utah\u27s problems of water use and water supply are becoming increasingly important. They are also becoming increasingly complex as competition for our water resources becomes more keen among various types of uses. In the formulation of plans for sound and efficient use of water it is essential to know the characteristics of occurrence and use of water supplies so that requirements can be balanced most effectively and economically against supply. This ordinarily requires basic hydrologic data to determine relations among climate, water losses, and water yield from watersheds. Such data are often unavailable - especially for the smaller basins and streams which characterize many parts of Utah. With greater emphasis on small watersheds and small project development, some way of estimating quantities and characteristics of streamflow which are vital to hydraulic design is essential. In spite of increased emphasis and expenditures for development of water, the expansion of basic data programs still lags behind actual development. At present, investigations and data gathering are not completely adequate to delineate the potential water resources nor to determine the extent of possible development. Without an expanded program of surface and underground water investigations, we cannot hope to outline our potentials completely. However, a broad picture of long-time average annual runoff, developed indirectly or from data at hand, should have considerable value in first stage planning on a statewide basis. The total hydrologic picture must be outlined to evaluate better the effect of individual project development on future regional development programs. Piecemeal development frequently does not fit into an ultimate patterns for most complete and efficient use of the water resource within a region or state. To avoid this kind of development, those responsible for formulating water programs and policies need all the hydrologic information they can get. Deficiencies of such information lend great emphasis to the need for developing dependable indirect methods and techniques to speed preliminary hydrologic surveys. This study was undertaken to develop techniques useful in making was undertaken to develop techniques useful in making rapid and economical estimates of water supplies. The study is restricted to the estimation of mean annual values. Much other information regarding extremes and variations is necessary for detailed project planning. The objective in this study, however, is to provide means of getting a broad perspective of the state\u27s water supply of sufficient accuracy for initial planning a regional nature