Semi-optimal Practicable Algorithmic Cooling

Algorithmic Cooling (AC) of spins applies entropy manipulation algorithms in open spin-systems in order to cool spins far beyond Shannon's entropy bound. AC of nuclear spins was demonstrated experimentally, and may contribute to nuclear magnetic resonance (NMR) spectroscopy. Several cooling algorithms were suggested in recent years, including practicable algorithmic cooling (PAC) and exhaustive AC. Practicable algorithms have simple implementations, yet their level of cooling is far from optimal; Exhaustive algorithms, on the other hand, cool much better, and some even reach (asymptotically) an optimal level of cooling, but they are not practicable. We introduce here semi-optimal practicable AC (SOPAC), wherein few cycles (typically 2-6) are performed at each recursive level. Two classes of SOPAC algorithms are proposed and analyzed. Both attain cooling levels significantly better than PAC, and are much more efficient than the exhaustive algorithms. The new algorithms are shown to bridge the gap between PAC and exhaustive AC. In addition, we calculated the number of spins required by SOPAC in order to purify qubits for quantum computation. As few as 12 and 7 spins are required (in an ideal scenario) to yield a mildly pure spin (60% polarized) from initial polarizations of 1% and 10%, respectively. In the latter case, about five more spins are sufficient to produce a highly pure spin (99.99% polarized), which could be relevant for fault-tolerant quantum computing.Comment: 13 pages, 5 figure

Analytical results for the distribution of shortest path lengths in random networks

We present two complementary analytical approaches for calculating the distribution of shortest path lengths in Erdos-R\'enyi networks, based on recursion equations for the shells around a reference node and for the paths originating from it. The results are in agreement with numerical simulations for a broad range of network sizes and connectivities. The average and standard deviation of the distribution are also obtained. In the case that the mean degree scales as $N^{\alpha}$ with the network size, the distribution becomes extremely narrow in the asymptotic limit, namely almost all pairs of nodes are equidistant, at distance $d=\lfloor 1/\alpha \rfloor$ from each other. The distribution of shortest path lengths between nodes of degree $m$ and the rest of the network is calculated. Its average is shown to be a monotonically decreasing function of $m$, providing an interesting relation between a local property and a global property of the network. The methodology presented here can be applied to more general classes of networks.Comment: 12 pages, 4 figures, accepted to EP

Quantum disentanglers

It is not possible to disentangle a qubit in an unknown state $|\psi>$ from a set of (N-1) ancilla qubits prepared in a specific reference state $|0>$. That is, it is not possible to {\em perfectly} perform the transformation $(|\psi,0...,0\r +|0,\psi,...,0\r +...+ |0,0,...\psi\r) \to |0,...,0>\otimes |\psi>$. The question is then how well we can do? We consider a number of different methods of extracting an unknown state from an entangled state formed from that qubit and a set of ancilla qubits in an known state. Measuring the whole system is, as expected, the least effective method. We present various quantum ``devices'' which disentangle the unknown qubit from the set of ancilla qubits. In particular, we present the optimal universal disentangler which disentangles the unknown qubit with the fidelity which does not depend on the state of the qubit, and a probabilistic disentangler which performs the perfect disentangling transformation, but with a probability less than one.Comment: 8 pages, 1 eps figur

Fiscal-capacity equalization-grants with taxpayers' lobbying

The economic analysis of tax-base equalization-grants from central to local governments suggests that the transfer mechanism distorts fiscal policies by providing incentives to local governments to set excessively high tax rates. In this paper, we extend the analysis by allowing taxpayers to lobby the policy makers for reductions of their own tax burdens. In principle, the distortions spurring from the lobbying activity should mitigate those caused by the equalization program. In contrast, we show that taxpayers lobbying amplifi es the distortions of the equalization mechanism. The degree of fiscal equalization can then be adjusted to alleviate the efficiency costs of lobbying

Gaia DR2 view of the Lupus V-VI clouds: the candidate diskless young stellar objects are mainly background contaminants

Extensive surveys of star-forming regions with Spitzer have revealed populations of disk-bearing young stellar objects. These have provided crucial constraints, such as the timescale of dispersal of protoplanetary disks, obtained by carefully combining infrared data with spectroscopic or X-ray data. While observations in various regions agree with the general trend of decreasing disk fraction with age, the Lupus V and VI regions appeared to have been at odds, having an extremely low disk fraction. Here we show, using the recent Gaia data release 2 (DR2), that these extremely low disk fractions are actually due to a very high contamination by background giants. Out of the 83 candidate young stellar objects (YSOs) in these clouds observed by Gaia, only five have distances of 150 pc, similar to YSOs in the other Lupus clouds, and have similar proper motions to other members in this star-forming complex. Of these five targets, four have optically thick (Class II) disks. On the one hand, this result resolves the conundrum of the puzzling low disk fraction in these clouds, while, on the other hand, it further clarifies the need to confirm the Spitzer selected diskless population with other tracers, especially in regions at low galactic latitude like Lupus V and VI. The use of Gaia astrometry is now an independent and reliable way to further assess the membership of candidate YSOs in these, and potentially other, star-forming regions.Comment: Accepted for publication on Astronomy&Astrophysics Letter

Nonlinear Qubit Transformations

We generalise our previous results of universal linear manipulations [Phys. Rev. A63, 032304 (2001)] to investigate three types of nonlinear qubit transformations using measurement and quantum based schemes. Firstly, nonlinear rotations are studied. We rotate different parts of a Bloch sphere in opposite directions about the z-axis. The second transformation is a map which sends a qubit to its orthogonal state (which we define as ORTHOG). We consider the case when the ORTHOG is applied to only a partial area of a Bloch sphere. We also study nonlinear general transformation, i.e. (theta,phi)->(theta-alpha,phi), again, applied only to part of the Bloch sphere. In order to achieve these three operations, we consider different measurement preparations and derive the optimal average (instead of universal) quantum unitary transformations. We also introduce a simple method for a qubit measurement and its application to other cases.Comment: minor corrections. To appear in PR

Design approaches in technology enhanced learning

Design is a critical to the successful development of any interactive learning environment (ILE). Moreover, in technology enhanced learning (TEL), the design process requires input from many diverse areas of expertise. As such, anyone undertaking tool development is required to directly address the design challenge from multiple perspectives. We provide a motivation and rationale for design approaches for learning technologies that draws upon Simon's seminal proposition of Design Science (Simon, 1969). We then review the application of Design Experiments (Brown, 1992) and Design Patterns (Alexander et al., 1977) and argue that a patterns approach has the potential to address many of the critical challenges faced by learning technologists

A novel quantum key distribution scheme with orthogonal product states

The general conditions for the orthogonal product states of the multi-state systems to be used in quantum key distribution (QKD) are proposed, and a novel QKD scheme with orthogonal product states in the 3x3 Hilbert space is presented. We show that this protocol has many distinct features such as great capacity, high efficiency. The generalization to nxn systems is also discussed and a fancy limitation for the eavesdropper's success probability is reached.Comment: 4 Pages, 3 Figure

Cytogenetic features of human trophoblast cell lines SWAN-71 and 3A-subE

Immortalization of primary cells with telomerase is thought to maintain normal phenotypic properties and avoid chromosomal abnormalities and other cancer-associated changes that occur following simian virus 40 tumor antigen (SV40 Tag) induced immortalization. However, we report that the human telomerase reverse transcriptase (hTERT)-immortalized SWAN-71 trophoblast cell line has a near pentaploid 103∼119,XXXX[cp20] karyotype. Additionally, DNA typing analysis indicated that SWAN-71 cells have acquired microsatellite instability. In comparison, the post-crisis SV40-transformed trophoblast cell line 3A-subE was hypertriploid 69∼81,XX[cp20]. Both cell lines contained multiple specific clonal rearrangements. These findings emphasize the need to monitor for genetic instability in hTERT-immortalized cells

Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

We find a Hermite-type basis for which the eigenvalue problem associated to the operator $H_{A,B}:=B(-\partial_x^2)+Ax^2$ acting on $L^2({\bf R};{\bf C}^2)$ becomes a three-terms recurrence. Here $A$ and $B$ are two constant positive definite matrices with no other restriction. Our main result provides an explicit characterization of the eigenvectors of $H_{A,B}$ that lie in the span of the first four elements of this basis when $AB\not= BA$.Comment: 11 pages, 1 figure. Some typos where corrected in this new versio