Conditional quantum one-time pad

Suppose that Alice and Bob are located in distant laboratories, which are connected by an ideal quantum channel. Suppose further that they share many copies of a quantum state $\rho_{ABE}$, such that Alice possesses the $A$ systems and Bob the $BE$ systems. In our model, there is an identifiable part of Bob's laboratory that is insecure: a third party named Eve has infiltrated Bob's laboratory and gained control of the $E$ systems. Alice, knowing this, would like use their shared state and the ideal quantum channel to communicate a message in such a way that Bob, who has access to the whole of his laboratory ($BE$ systems), can decode it, while Eve, who has access only to a sector of Bob's laboratory ($E$ systems) and the ideal quantum channel connecting Alice to Bob, cannot learn anything about Alice's transmitted message. We call this task the conditional one-time pad, and in this paper, we prove that the optimal rate of secret communication for this task is equal to the conditional quantum mutual information $I(A;B|E)$ of their shared state. We thus give the conditional quantum mutual information an operational meaning that is different from those given in prior works, via state redistribution, conditional erasure, or state deconstruction. We also generalize the model and method in several ways, one of which demonstrates that the negative tripartite interaction information $-I_{3}(A;B;E) = I(A;BE)-I(A;B)-I(A;E)$ of a tripartite state $\rho_{ABE}$ is an achievable rate for a secret-sharing task, i.e., the case in which Alice's message should be secure from someone possessing only the $AB$ or $AE$ systems but should be decodable by someone possessing all systems $A$, $B$, and $E$.Comment: v2: 16 pages, final version accepted for publication in Physical Review Letter

The chain rule implies Tsirelson's bound: an approach from generalized mutual information

In order to analyze an information theoretical derivation of Tsirelson's bound based on information causality, we introduce a generalized mutual information (GMI), defined as the optimal coding rate of a channel with classical inputs and general probabilistic outputs. In the case where the outputs are quantum, the GMI coincides with the quantum mutual information. In general, the GMI does not necessarily satisfy the chain rule. We prove that Tsirelson's bound can be derived by imposing the chain rule on the GMI. We formulate a principle, which we call the no-supersignalling condition, which states that the assistance of nonlocal correlations does not increase the capability of classical communication. We prove that this condition is equivalent to the no-signalling condition. As a result, we show that Tsirelson's bound is implied by the nonpositivity of the quantitative difference between information causality and no-supersignalling.Comment: 23 pages, 8 figures, Added Section 2 and Appendix B, result unchanged, Added reference

Photoreceptor spectral sensitivities of the Small White butterfly Pieris rapae crucivora interpreted with optical modeling

The compound eye of the Small White butterfly, Pieris rapae crucivora, has four classes of visual pigments, with peak absorption in the ultraviolet, violet, blue and green, but electrophysiological recordings yielded eight photoreceptors classes: an ultraviolet, violet, blue, double-peaked blue, green, blue-suppressed-green, pale-red and deep-red class. These photoreceptor classes were identified in three types of ommatidia, distinguishable by the different eye shine spectra and fluorescence; the latter only being present in the eyes of males. We present here two slightly different optical models that incorporate the various visual pigments, the light-filtering actions of the fluorescent, pale-red and deep-red screening pigment, located inside or adjacent to the rhabdom, and the reflectance spectrum of the tapetum that abuts the rhabdom proximally. The models serve to explain the photoreceptor spectral sensitivities as well as the eye shine

Photoreceptor Spectral Sensitivity in the Bumblebee, Bombus impatiens (Hymenoptera: Apidae)

The bumblebee Bombus impatiens is increasingly used as a model in comparative studies of colour vision, or in behavioural studies relying on perceptual discrimination of colour. However, full spectral sensitivity data on the photoreceptor inputs underlying colour vision are not available for B. impatiens. Since most known bee species are trichromatic, with photoreceptor spectral sensitivity peaks in the UV, blue and green regions of the spectrum, data from a related species, where spectral sensitivity measurements have been made, are often applied to B impatiens. Nevertheless, species differences in spectral tuning of equivalent photoreceptor classes may result in peaks that differ by several nm, which may have small but significant effects on colour discrimination ability. We therefore used intracellular recording to measure photoreceptor spectral sensitivity in B. impatiens. Spectral peaks were estimated at 347, 424 and 539 nm for UV, blue and green receptors, respectively, suggesting that this species is a UV-blue-green trichromat. Photoreceptor spectral sensitivity peaks are similar to previous measurements from Bombus terrestris, although there is a significant difference in the peak sensitivity of the blue receptor, which is shifted in the short wave direction by 12–13 nm in B. impatiens compared to B. terrestris

Spectral reflectance properties of iridescent pierid butterfly wings

The wings of most pierid butterflies exhibit a main, pigmentary colouration: white, yellow or orange. The males of many species have in restricted areas of the wing upper sides a distinct structural colouration, which is created by stacks of lamellae in the ridges of the wing scales, resulting in iridescence. The amplitude of the reflectance is proportional to the number of lamellae in the ridge stacks. The angle-dependent peak wavelength of the observed iridescence is in agreement with classical multilayer theory. The iridescence is virtually always in the ultraviolet wavelength range, but some species have a blue-peaking iridescence. The spectral properties of the pigmentary and structural colourations are presumably tuned to the spectral sensitivities of the butterflies’ photoreceptors

Mechanisms, functions and ecology of colour vision in the honeybee.

notes: PMCID: PMC4035557types: Journal Article© The Author(s) 2014.This is an open access article that is freely available in ORE or from Springerlink.com. Please cite the published version available at: http://link.springer.com/article/10.1007%2Fs00359-014-0915-1Research in the honeybee has laid the foundations for our understanding of insect colour vision. The trichromatic colour vision of honeybees shares fundamental properties with primate and human colour perception, such as colour constancy, colour opponency, segregation of colour and brightness coding. Laborious efforts to reconstruct the colour vision pathway in the honeybee have provided detailed descriptions of neural connectivity and the properties of photoreceptors and interneurons in the optic lobes of the bee brain. The modelling of colour perception advanced with the establishment of colour discrimination models that were based on experimental data, the Colour-Opponent Coding and Receptor Noise-Limited models, which are important tools for the quantitative assessment of bee colour vision and colour-guided behaviours. Major insights into the visual ecology of bees have been gained combining behavioural experiments and quantitative modelling, and asking how bee vision has influenced the evolution of flower colours and patterns. Recently research has focussed on the discrimination and categorisation of coloured patterns, colourful scenes and various other groupings of coloured stimuli, highlighting the bees' behavioural flexibility. The identification of perceptual mechanisms remains of fundamental importance for the interpretation of their learning strategies and performance in diverse experimental tasks.Biotechnology and Biological Sciences Research Council (BBSRC

Metarhodopsin control by arrestin, light-filtering screening pigments, and visual pigment turnover in invertebrate microvillar photoreceptors

The visual pigments of most invertebrate photoreceptors have two thermostable photo-interconvertible states, the ground state rhodopsin and photo-activated metarhodopsin, which triggers the phototransduction cascade until it binds arrestin. The ratio of the two states in photoequilibrium is determined by their absorbance spectra and the effective spectral distribution of illumination. Calculations indicate that metarhodopsin levels in fly photoreceptors are maintained below ~35% in normal diurnal environments, due to the combination of a blue-green rhodopsin, an orange-absorbing metarhodopsin and red transparent screening pigments. Slow metarhodopsin degradation and rhodopsin regeneration processes further subserve visual pigment maintenance. In most insect eyes, where the majority of photoreceptors have green-absorbing rhodopsins and blue-absorbing metarhodopsins, natural illuminants are predicted to create metarhodopsin levels greater than 60% at high intensities. However, fast metarhodopsin decay and rhodopsin regeneration also play an important role in controlling metarhodopsin in green receptors, resulting in a high rhodopsin content at low light intensities and a reduced overall visual pigment content in bright light. A simple model for the visual pigment–arrestin cycle is used to illustrate the dependence of the visual pigment population states on light intensity, arrestin levels and pigment turnover

Journeys from quantum optics to quantum technology

Sir Peter Knight is a pioneer in quantum optics which has now grown to an important branch of modern physics to study the foundations and applications of quantum physics. He is leading an effort to develop new technologies from quantum mechanics. In this collection of essays, we recall the time we were working with him as a postdoc or a PhD student and look at how the time with him has influenced our research