A simple construction of complex equiangular lines

A set of vectors of equal norm in $\mathbb{C}^d$ represents equiangular lines if the magnitudes of the inner product of every pair of distinct vectors in the set are equal. The maximum size of such a set is $d^2$, and it is conjectured that sets of this maximum size exist in $\mathbb{C}^d$ for every $d \geq 2$. We describe a new construction for maximum-sized sets of equiangular lines, exposing a previously unrecognized connection with Hadamard matrices. The construction produces a maximum-sized set of equiangular lines in dimensions 2, 3 and 8.Comment: 11 pages; minor revisions and comments added in section 1 describing a link to previously known results; correction to Theorem 1 and updates to reference

A Quantum-Bayesian Route to Quantum-State Space

In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent's personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the usual probability rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper, we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum Bayesianism. The starting point is the representation of quantum states induced by a symmetric informationally complete measurement or SIC. In this representation, the Born rule takes the form of a particularly simple modification of the law of total probability. We show how to derive key features of quantum-state space from (i) the requirement that the Born rule arises as a simple modification of the law of total probability and (ii) a limited number of additional assumptions of a strong Bayesian flavor.Comment: 7 pages, 1 figure, to appear in Foundations of Physics; this is a condensation of the argument in arXiv:0906.2187v1 [quant-ph], with special attention paid to making all assumptions explici

Complementarity and the uncertainty relations

We formulate a general complementarity relation starting from any Hermitian operator with discrete non-degenerate eigenvalues. We then elucidate the relationship between quantum complementarity and the Heisenberg-Robertson's uncertainty relation. We show that they are intimately connected. Finally we exemplify the general theory with some specific suggested experiments.Comment: 9 pages, 4 figures, REVTeX, uses epsf.sty and multicol.st

Bohmian mechanics, the quantum-classical correspondence and the classical limit: the case of the square billiard

Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum amplitude being controlled by the spread of the corresponding classical statistical distribution. We investigate wavepacket dynamics and compute the corresponding de Broglie-Bohm trajectories in the quantum square billiard. We also determine the trajectories and statistical distribution dynamics for the equivalent classical billiard. Individual Bohmian trajectories follow the streamlines of the probability flow and are generically non-classical. This can also hold even for short times, when the wavepacket is still localized along a classical trajectory. This generic feature of Bohmian trajectories is expected to hold in the classical limit. We further argue that in this context decoherence cannot constitute a viable solution in order to recover classicality.Comment: Figures downgraded to low resolution; To be published in Found. Phys. (2009)

Finite-precision measurement does not nullify the Kochen-Specker theorem

It is proven that any hidden variable theory of the type proposed by Meyer [Phys. Rev. Lett. {\bf 83}, 3751 (1999)], Kent [{\em ibid.} {\bf 83}, 3755 (1999)], and Clifton and Kent [Proc. R. Soc. London, Ser. A {\bf 456}, 2101 (2000)] leads to experimentally testable predictions that are in contradiction with those of quantum mechanics. Therefore, it is argued that the existence of dense Kochen-Specker-colorable sets must not be interpreted as a nullification of the physical impact of the Kochen-Specker theorem once the finite precision of real measurements is taken into account.Comment: REVTeX4, 5 page

Greenberger-Horne-Zeilinger-like proof of Bell's theorem involving observers who do not share a reference frame

Vaidman described how a team of three players, each of them isolated in a remote booth, could use a three-qubit Greenberger-Horne-Zeilinger state to always win a game which would be impossible to always win without quantum resources. However, Vaidman's method requires all three players to share a common reference frame; it does not work if the adversary is allowed to disorientate one player. Here we show how to always win the game, even if the players do not share any reference frame. The introduced method uses a 12-qubit state which is invariant under any transformation $R_a \otimes R_b \otimes R_c$ (where $R_a = U_a \otimes U_a \otimes U_a \otimes U_a$, where $U_j$ is a unitary operation on a single qubit) and requires only single-qubit measurements. A number of further applications of this 12-qubit state are described.Comment: REVTeX4, 6 pages, 1 figur

Biometrics beyond the visible spectrum: Imaging technologies and applications

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-04391-8_20Proceedings of Joint COST 2101 and 2102 International Conference, BioID_MultiComm 2009, Madrid (Spain)Human body images acquired at visible spectrum have inherent restrictions that hinder the performance of person recognition systems built using that kind of information (e.g. scene artefacts under varying illumination conditions). One promising approach for dealing with those limitations is using images acquired beyond the visible spectrum. This paper reviews some of the existing human body imaging technologies working beyond the visible spectrum (X-ray, Infrared, Millimeter and Submillimeter Wave imaging technologies). The benefits and drawbacks of each technology and their biometric applications are presented.This work has been supported by Terasense (CSD2008-00068) Consolider project of the Spanish Ministry of Science and Technology

Time-of-arrival distributions from position-momentum and energy-time joint measurements

The position-momentum quasi-distribution obtained from an Arthurs and Kelly joint measurement model is used to obtain indirectly an ``operational'' time-of-arrival (TOA) distribution following a quantization procedure proposed by Kocha\'nski and W\'odkiewicz [Phys. Rev. A 60, 2689 (1999)]. This TOA distribution is not time covariant. The procedure is generalized by using other phase-space quasi-distributions, and sufficient conditions are provided for time covariance that limit the possible phase-space quasi-distributions essentially to the Wigner function, which, however, provides a non-positive TOA quasi-distribution. These problems are remedied with a different quantization procedure which, on the other hand, does not guarantee normalization. Finally an Arthurs and Kelly measurement model for TOA and energy (valid also for arbitrary conjugate variables when one of the variables is bounded from below) is worked out. The marginal TOA distribution so obtained, a distorted version of Kijowski's distribution, is time covariant, positive, and normalized

Ruthenium-rhenium and ruthenium-palladium supramolecular photocatalysts for photoelectrocatalytic CO2 and H+ reduction.

Photoelectrocatalysis offers the opportunity to close the carbon loop and convert captured CO2 back into useful fuels and feedstocks, mitigating against anthropogenic climate change. However, since CO2 is inherently stable and sunlight is a diffuse and intermittent energy source, there are considerable scientific challenges to overcome. In this paper we present the integration of two new metal–organic photocatalysts into photocathodes for the reduction of CO2 using ambient light. The two molecular dyads contained a rhenium carbonyl or palladium-based catalytic centre bridged to a ruthenium bipyridyl photosensitizer functionalised with carboxylic acid groups to enable adsorption onto the surface of mesoporous NiO cathodes. The photocathodes were evaluated for photoelectrochemical reduction of CO2 to CO or H+ to H2 and the performances were compared directly with a control compound lacking the catalytic site. A suite of electrochemical, UV-visible steady-state/time-resolved spectroscopy, X-ray photoelectron spectroscopy and gas chromatography measurements were employed to gain kinetic and mechanistic insight to primary electron transfer processes and relate the structure to the photoelectrocatalytic performance under various conditions in aqueous media. A change in behaviour when the photocatalysts were immobilized on NiO was observed. Importantly, the transfer of electron density towards the Re–CO catalytic centre was observed, using time resolved infrared spectroscopy, only when the photocatalyst was immobilized on NiO and not in MeCN solution. We observed that photocurrent and gaseous photoproduct yields are limited by a relatively low yield of the required charge-separated state across the NiO|Photocatalyst interface. Nonetheless, the high faradaic efficiency (94%) and selectivity (99%) of the Re system towards CO evolution are very promising

Measurements of long-range near-side angular correlations in sNN=5\sqrt{s_{\text{NN}}}=5TeV proton-lead collisions in the forward region

Two-particle angular correlations are studied in proton-lead collisions at a nucleon-nucleon centre-of-mass energy of $\sqrt{s_{\text{NN}}}=5$TeV, collected with the LHCb detector at the LHC. The analysis is based on data recorded in two beam configurations, in which either the direction of the proton or that of the lead ion is analysed. The correlations are measured in the laboratory system as a function of relative pseudorapidity, $\Delta\eta$, and relative azimuthal angle, $\Delta\phi$, for events in different classes of event activity and for different bins of particle transverse momentum. In high-activity events a long-range correlation on the near side, $\Delta\phi \approx 0$, is observed in the pseudorapidity range $2.0<\eta<4.9$. This measurement of long-range correlations on the near side in proton-lead collisions extends previous observations into the forward region up to $\eta=4.9$. The correlation increases with growing event activity and is found to be more pronounced in the direction of the lead beam. However, the correlation in the direction of the lead and proton beams are found to be compatible when comparing events with similar absolute activity in the direction analysed.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-040.htm