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

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

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

Quantum Cryptography Based on the Time--Energy Uncertainty Relation

A new cryptosystem based on the fundamental time--energy uncertainty relation is proposed. Such a cryptosystem can be implemented with both correlated photon pairs and single photon states.Comment: 5 pages, LaTex, no figure

Microcurrent stimulation in the treatment of dry and wet macular degeneration

Purpose: To determine the safety and efficacy of the application of transcutaneous (transpalpebral) microcurrent stimulation to slow progression of dry and wet macular degeneration or improve vision in dry and wet macular degeneration. Methods: Seventeen patients aged between 67 and 95 years with an average age of 83 years were selected to participate in the study over a period of 3 months in two eye care centers. There were 25 eyes with dry age-related macular degeneration (DAMD) and six eyes with wet age-related macular degeneration (WAMD). Frequency-specific microcurrent stimulation was applied in a transpalpebral manner, using two programmable dual channel microcurrent units delivering pulsed microcurrent at 150 μA for 35 minutes once a week. The frequency pairs selected were based on targeting tissues, which are typically affected by the disease combined with frequencies that target disease processes. Early Treatment Diabetic Retinopathy Study or Snellen visual acuity (VA) was measured before and after each treatment session. All treatment was administered in a clinical setting. Results: Significant increases were seen in VA in DAMD (P=0.012, Wilcoxon one-sample test), but in WAMD, improvements did not reach statistical significance (P=0.059). In DAMD eyes, twice as many patients showed increase in VA (52%) compared to those showing dete-rioration (26%), with improvements being often sizeable, whereas deteriorations were usually very slight. In WAMD eyes, five of six (83%) patients showed an increase and none showed deterioration. Conclusion: The substantial changes observed over this period, combined with continued improvement for patients who continued treatment once a month, are encouraging for future studies. The changes observed indicate the potential efficacy of microcurrent to delay degeneration and possibly improve age-related macular degeneration, both wet and dry. However, this study has no control arm, so results should be treated with caution. Randomized double-blind controlled studies are needed to determine long-term effects

Scaling Property of the global string in the radiation dominated universe

We investigate the evolution of the global string network in the radiation dominated universe by use of numerical simulations in 3+1 dimensions. We find that the global string network settles down to the scaling regime where the energy density of global strings, $\rho_{s}$, is given by $\rho_{s} = \xi \mu / t^2$ with $\mu$ the string tension per unit length and the scaling parameter, $\xi \sim (0.9-1.3)$, irrespective of the cosmic time. We also find that the loop distribution function can be fitted with that predicted by the so-called one scale model. Concretely, the number density, $n_{l}(t)$, of the loop with the length, $l$, is given by $n_{l}(t) = \nu/[t^{3/2} (l + \kappa t)^{5/2}]$ where $\nu \sim 0.0865$ and $\kappa$ is related with the Nambu-Goldstone(NG) boson radiation power from global strings, $P$, as $P = \kappa \mu$ with $\kappa \sim 0.535$. Therefore, the loop production function also scales and the typical scale of produced loops is nearly the horizon distance. Thus, the evolution of the global string network in the radiation dominated universe can be well described by the one scale model in contrast with that of the local string network.Comment: 18 pages, 9 figures, to appear in Phys. Rev.

Affine Constellations Without Mutually Unbiased Counterparts

It has been conjectured that a complete set of mutually unbiased bases in a space of dimension d exists if and only if there is an affine plane of order d. We introduce affine constellations and compare their existence properties with those of mutually unbiased constellations, mostly in dimension six. The observed discrepancies make a deeper relation between the two existence problems unlikely.Comment: 8 page

Acceptability, usability and performance of lateral flow immunoassay tests for SARS-CoV-2 antibodies: REACT-2 study of self-testing in non-healthcare key workers

Background Seroprevalence studies are essential to understand the epidemiology of SARS-CoV-2. Various technologies, including laboratory assays and point-of-care self-tests, are available for antibody testing. The interpretation of seroprevalence studies requires comparative data on the performance of antibody tests. Methods In June 2020, current and former members of the UK Police forces and Fire service performed a self-test lateral flow immunoassay (LFIA), had a nurse-performed LFIA and provided a venous blood sample for ELISA . We present the prevalence of antibodies to SARS-CoV-2; the acceptability and usability of self-test LFIAs; and determine the sensitivity and specificity of LFIAs compared to laboratory ELISA. Results In this cohort of 5189 current and former members of the Police service and 263 members of the Fire service, 7.4% (396/5,348; 95% CI, 6.7-8.1) were antibody positive. Seroprevalence was 8.9% (6.9-11.4) in those under 40 years, 11.5% (8.8-15.0) in those of non-white ethnicity and 7.8% (7.1-8.7) in those currently working. Self-test LFIA had an acceptability of 97.7% and a usability of 90.0%. There was substantial agreement between within-participant LFIA results (kappa 0.80; 0.77-0.83). The LFIAs had a similar performance: compared to ELISA, sensitivity was 82.1% (77.7-86.0) self-test and 76.4% (71.9-80.5) nurse-performed with specificity of 97.8% (97.3-98.2) and 98.5% (98.1-98.8) respectively. Conclusion A greater proportion of this non-healthcare key worker cohort showed evidence of previous infection with SARS-CoV-2 than the general population at 6.0% (5.8-6.1) following the first wave in England. The high acceptability and usability reported by participants and similar performance of self-test and nurse-performed LFIAs indicate that the self-test LFIA is fit for purpose for home-testing in occupational and community prevalence studies