Coherent transport on Apollonian networks and continuous-time quantum walks

We study the coherent exciton transport on Apollonian networks generated by simple iterative rules. The coherent exciton dynamics is modeled by continuous-time quantum walks and we calculate the transition probabilities between two nodes of the networks. We find that the transport depends on the initial nodes of the excitation. For networks less than the second generation the coherent transport shows perfect revivals when the initial excitation starts at the central node. For networks of higher generation, the transport only shows partial revivals. Moreover, we find that the excitation is most likely to be found at the initial nodes while the coherent transport to other nodes has a very low probability. In the long time limit, the transition probabilities show characteristic patterns with identical values of limiting probabilities. Finally, the dynamics of quantum transport are compared with the classical transport modeled by continuous-time random walks.Comment: 5 pages, 6 figues. Submitted to Phys. ReV.

Conditional Quantum Walk and Iterated Quantum Games

Iterated bipartite quantum games are implemented in terms of the discrete-time quantum walk on the line. Our proposal allows for conditional strategies, as two rational agents make a choice from a restricted set of two-qubit unitary operations. Several frequently used classical strategies give rise to families of corresponding quantum strategies. A quantum version of the Prisoner's Dilemma in which both players use mixed strategies is presented as a specific example. Since there are now quantum walk physical implementations at a proof-of principle stage, this connection may represent a step towards the experimental realization of quantum games.Comment: Revtex 4, 6 pages, 3 figures. Expanded version with one more figure and updated references. Abstract was rewritte

A Quantum Lovasz Local Lemma

The Lovasz Local Lemma (LLL) is a powerful tool in probability theory to show the existence of combinatorial objects meeting a prescribed collection of "weakly dependent" criteria. We show that the LLL extends to a much more general geometric setting, where events are replaced with subspaces and probability is replaced with relative dimension, which allows to lower bound the dimension of the intersection of vector spaces under certain independence conditions. Our result immediately applies to the k-QSAT problem: For instance we show that any collection of rank 1 projectors with the property that each qubit appears in at most $2^k/(e \cdot k)$ of them, has a joint satisfiable state. We then apply our results to the recently studied model of random k-QSAT. Recent works have shown that the satisfiable region extends up to a density of 1 in the large k limit, where the density is the ratio of projectors to qubits. Using a hybrid approach building on work by Laumann et al. we greatly extend the known satisfiable region for random k-QSAT to a density of $\Omega(2^k/k^2)$. Since our tool allows us to show the existence of joint satisfying states without the need to construct them, we are able to penetrate into regions where the satisfying states are conjectured to be entangled, avoiding the need to construct them, which has limited previous approaches to product states.Comment: 19 page

Continuous-time quantum walks on one-dimension regular networks

In this paper, we consider continuous-time quantum walks (CTQWs) on one-dimension ring lattice of N nodes in which every node is connected to its 2m nearest neighbors (m on either side). In the framework of the Bloch function ansatz, we calculate the spacetime transition probabilities between two nodes of the lattice. We find that the transport of CTQWs between two different nodes is faster than that of the classical continuous-time random walk (CTRWs). The transport speed, which is defined by the ratio of the shortest path length and propagating time, increases with the connectivity parameter m for both the CTQWs and CTRWs. For fixed parameter m, the transport of CTRWs gets slow with the increase of the shortest distance while the transport (speed) of CTQWs turns out to be a constant value. In the long time limit, depending on the network size N and connectivity parameter m, the limiting probability distributions of CTQWs show various paterns. When the network size N is an even number, the probability of being at the original node differs from that of being at the opposite node, which also depends on the precise value of parameter m.Comment: Typos corrected and Phys. ReV. E comments considered in this versio

Schaffenrathʼs Inscription Column in Pisani rov, Postojnska jama

Napisi lahko pripomorejo k razjasnitvi nezadostno dokumentirane zgodovine odkrivanja glavnih rovov Postojnske jame. Ta čas je bil povezan s tremi osebami: Josipom Jeršinovičem plemenitim Löwengreif, Alojzom Schaffenrathom in grofom Francem Hohenwartom. Temelječ na sodobnih zapisih Schaffenratha (1834), Hohenwarta (1830, 1832a,b) in Schmidla (1854), avtorji razpravljajo o okoliščinah in času njihovih raziskovanj glavne jame ter menijo, da ta ni bila odkrita do prihoda nadvojvode Ferdinanda avgusta 1819. Eden najstarejših napisov iz tega časa je na kapniškem stebru v Pisanem rovu, 90 m od tam, kjer se odcepi od glavnega rova. Tu je Schaffenrath 1825 zapisal imeni Löwengreifa, Gospodaritscha in svoje. Ta steber je morda edino mesto v Postojnski jami, kjer so vsa tri imena skupaj. Če upoštevamo razmeroma pozne raziskave glavnega rova, je letnica 1825 morda leto odkritja tega dela jame. To potrjuje tudi dejstvo, da tega dela jame ni na prvem objavljenem zemljevidu (Bronn, 1826, temelječ na zemljevidu Foÿker/Schaffenrath iz okoli 1821). 1832 je bil odprt notranji del Pisanega rova in imenovan v čast nadvojvode Janeza. Na steber so dodali še več napisov, več pa jih je tudi dalje po rovu. Iz 1836 je podpis J(ozef) Hauer, to je paleontolog in oče Franca plemenitega Hauerja. Tudi Anton Perko, mlajši brat Ivana Andreja, je zapustil svoje ime. I.A. Perko je podpisan 1892 v Rovu brez imena, v letu preden so on, njegov brat in drugi v Trstu ustanovili študentsko jamarsko društvo “Hades”. Raziskovanje in dokumentiranje zgodovinskih napisov lahko pomaga pri rekonstrukciji in razlagi zgodovine raziskav in odkrivanj te najpomembnejše turistične jame.Inscriptions may help to clarify the incompletely documented early history of the discovery of the main passages in Postojnska jama. This period is associated with three people: Josef (Josip) Jeršinovič Ritter von Löwengreif, Alois Schaffenrath, and Franz Graf von Hohenwart. Based on the contemporary writings of Schaffenrath (1834), Hohenwart (1830, 1832a,b) and Schmidl (1854) the authors discuss the circumstances and timing of the exploration of the main cave, suggesting that the main passage was not discovered until after the visit of Erzherzog Ferdinand in August 1819. One of the earliest inscriptions from that period is found on a column in Pisani rov, 90 m from its branch from the main passage. Here Schaffenrath left in 1825 the names of Löwengreif, of Gospodaritsch, and of himself. This column may be the only site in Postojnska jama featuring all three names in one place. In view of the rather late exploration of the main passage, the date 1825 may be the discovery date of this section of the cave since it does not appear on the earliest map published (Bronn, 1826, based on a map of Foÿker/Schaffenrath ca. 1821). In 1832 the back part of Pisani rov was opened and named in honour of Erzherzog Johann. Several more inscriptions were placed on the column. Further down the passage a few more inscriptions exist. One was dated 1836 by J(ozef) Hauer, a paleontologist and the father of Franz Ritter von Hauer. Also Anton Perko, the younger brother of Ivan Andrej Perko left his name. I.A. Perko signed as well, but in the Rov brez imena, in the year 1892, a year before he, his brother and others founded the student caversʼ club “Hades” in Trieste. Search and documentation of historic inscriptions may therefore aid in reconstructing the exploration and visitation history of this most important show cave

Crystal structure of (η4-cycloocta-1,5-dien)(1,2-bis(diethylphosphino)-ethane)rhodium(I) tetrafluoroborate, [Rh(C8H12(C10H24P2)]BF4)

C18H36BF4P2RI1, monoclinic, P121/n1 (no. 14), a = 15.522(3) Å, b = 9.173(2) Å, c = 15.862(3) Å, β = 103.91(3)°, V= 2192.3 Å3, Z = 4, Rgt(F) = 0.037, wRref(F2) = 0.087, T=200 K