Daughter of Love : Waltzes

https://digitalcommons.library.umaine.edu/mmb-ps/3450/thumbnail.jp

Using of small-scale quantum computers in cryptography with many-qubit entangled states

We propose a new cryptographic protocol. It is suggested to encode information in ordinary binary form into many-qubit entangled states with the help of a quantum computer. A state of qubits (realized, e.g., with photons) is transmitted through a quantum channel to the addressee, who applies a quantum computer tuned to realize the inverse unitary transformation decoding of the message. Different ways of eavesdropping are considered, and an estimate of the time needed for determining the secret unitary transformation is given. It is shown that using even small quantum computers can serve as a basis for very efficient cryptographic protocols. For a suggested cryptographic protocol, the time scale on which communication can be considered secure is exponential in the number of qubits in the entangled states and in the number of gates used to construct the quantum network

Drilling into a deep buried valley (ICDP DOVE): a 252 m long sediment succession from a glacial overdeepening in northwestern Switzerland

The modern Alpine landscape and its foreland were strongly impacted by the numerous glacier ad- vance and retreat cycles during the Middle-to-Late Pleistocene. Due to the overall erosive character of each glaciation cycle, however, direct traces of older glaciations tend to be poorly preserved within the formerly glaciated domains of the pan-Alpine area. Nevertheless, sediments of older glaciations may occur hidden un- der the modern surface in buried glacially overdeepened troughs that reach below the normal level of fluvial erosion (fluvial base level). These sedimentary archives, partly dating back to the Middle Pleistocene period, are of great scientific value for reconstructing the timing and extent of extensive Alpine glaciation, paleocli- mate, and paleoenvironmental changes in the past and help to better understand ongoing and future changes in the pan-Alpine area. Therefore, the International Continental Scientific Drilling Program (ICDP) project DOVE (Drilling Overdeepened Alpine Valleys) targets several of these glacial overdeepened sedimentary basins to re- cover their sedimentary infills. In the frame of the DOVE project, a 252 m long drill core of unconsolidated Quaternary sediments was recovered in northern Switzerland from an over 300 m deep glacially overdeepened structure (“Basadingen Trough”) formed by the former Rhine Glacier lobe system. The recovered sedimentary succession was divided into three stratigraphic units on the basis of lithological and petrophysical characteristics. The lowest unit, deposited below the fluvial base level, consists of an over 200 m thick succession of glacial to (glacio)lacustrine sediments and contains remains of possibly two glaciation cycles. Overlying this lowermost succession, an ∼ 37 m thick fluvial-to-glaciofluvial gravel deposit occurs, which correlates to a locally outcrop- ping Middle Pleistocene formation (“Buechberg Gravel Complex”). The sediment succession is capped by an ∼ 11 m thick diamictic succession interpreted as the subglacial till from the later extensive glaciation, including the regional glaciation during the Last Glacial Maximum. The recovered sediment succession thus supports the proposed multi-phase origin of trough formation and its infill

Quantum complexities of ordered searching, sorting, and element distinctness

We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list, we prove a lower bound of \frac{1}{\pi}(\ln(N)-1) accesses to the list elements for ordered searching, a lower bound of \Omega(N\log{N}) binary comparisons for sorting, and a lower bound of \Omega(\sqrt{N}\log{N}) binary comparisons for element distinctness. The previously best known lower bounds are {1/12}\log_2(N) - O(1) due to Ambainis, \Omega(N), and \Omega(\sqrt{N}), respectively. Our proofs are based on a weighted all-pairs inner product argument. In addition to our lower bound results, we give a quantum algorithm for ordered searching using roughly 0.631 \log_2(N) oracle accesses. Our algorithm uses a quantum routine for traversing through a binary search tree faster than classically, and it is of a nature very different from a faster algorithm due to Farhi, Goldstone, Gutmann, and Sipser.Comment: This new version contains new results. To appear at ICALP '01. Some of the results have previously been presented at QIP '01. This paper subsumes the papers quant-ph/0009091 and quant-ph/000903

Quantum state transfer and entanglement distribution among distant nodes in a quantum network

We propose a scheme to utilize photons for ideal quantum transmission between atoms located at spatially-separated nodes of a quantum network. The transmission protocol employs special laser pulses which excite an atom inside an optical cavity at the sending node so that its state is mapped into a time-symmetric photon wavepacket that will enter a cavity at the receiving node and be absorbed by an atom there with unit probability. Implementation of our scheme would enable reliable transfer or sharing of entanglement among spatially distant atoms.Comment: 4 pages, 3 postscript figure

Autonomous three-dimensional formation flight for a swarm of unmanned aerial vehicles

This paper investigates the development of a new guidance algorithm for a formation of unmanned aerial vehicles. Using the new approach of bifurcating potential fields, it is shown that a formation of unmanned aerial vehicles can be successfully controlled such that verifiable autonomous patterns are achieved, with a simple parameter switch allowing for transitions between patterns. The key contribution that this paper presents is in the development of a new bounded bifurcating potential field that avoids saturating the vehicle actuators, which is essential for real or safety-critical applications. To demonstrate this, a guidance and control method is developed, based on a six-degreeof-freedom linearized aircraft model, showing that, in simulation, three-dimensional formation flight for a swarm of unmanned aerial vehicles can be achieved

Experimental measurement-device-independent verification of quantum steering

Bell non-locality between distant quantum systems-that is, joint correlations which violate a Bell inequality-can be verified without trusting the measurement devices used, nor those performing the measurements. This leads to unconditionally secure protocols for quantum information tasks such as cryptographic key distribution. However, complete verification of Bell non-locality requires high detection efficiencies, and is not robust to typical transmission losses over long distances. In contrast, quantum or Einstein-Podolsky-Rosen steering, a weaker form of quantum correlation, can be verified for arbitrarily low detection efficiencies and high losses. The cost is that current steering-verification protocols require complete trust in one of the measurement devices and its operator, allowing only one-sided secure key distribution. Here we present measurement-device-independent steering protocols that remove this need for trust, even when Bell non-locality is not present. We experimentally demonstrate this principle for singlet states and states that do not violate a Bell inequality.Australian Research Council/140100648Marie-Curie Fellowshi

Geometry of the 3-Qubit State, Entanglement and Division Algebras

We present a generalization to 3-qubits of the standard Bloch sphere representation for a single qubit and of the 7-dimensional sphere representation for 2 qubits presented in Mosseri {\it et al.}\cite{Mosseri2001}. The Hilbert space of the 3-qubit system is the 15-dimensional sphere $S^{15}$, which allows for a natural (last) Hopf fibration with $S^8$ as base and $S^7$ as fiber. A striking feature is, as in the case of 1 and 2 qubits, that the map is entanglement sensitive, and the two distinct ways of un-entangling 3 qubits are naturally related to the Hopf map. We define a quantity that measures the degree of entanglement of the 3-qubit state. Conjectures on the possibility to generalize the construction for higher qubit states are also discussed.Comment: 12 pages, 2 figures, final versio