Trade-off coding for universal qudit cloners motivated by the Unruh effect

A "triple trade-off" capacity region of a noisy quantum channel provides a more complete description of its capabilities than does a single capacity formula. However, few full descriptions of a channel's ability have been given due to the difficult nature of the calculation of such regions---it may demand an optimization of information-theoretic quantities over an infinite number of channel uses. This work analyzes the d-dimensional Unruh channel, a noisy quantum channel which emerges in relativistic quantum information theory. We show that this channel belongs to the class of quantum channels whose capacity region requires an optimization over a single channel use, and as such is tractable. We determine two triple-trade off regions, the quantum dynamic capacity region and the private dynamic capacity region, of the d-dimensional Unruh channel. Our results show that the set of achievable rate triples using this coding strategy is larger than the set achieved using a time-sharing strategy. Furthermore, we prove that the Unruh channel has a distinct structure made up of universal qudit cloning channels, thus providing a clear relationship between this relativistic channel and the process of stimulated emission present in quantum optical amplifiers.Comment: 26 pages, 4 figures; v2 has minor corrections to Definition 2. Definition 4 and Remark 5 have been adde

Trade-off capacities of the quantum Hadamard channels

Coding theorems in quantum Shannon theory express the ultimate rates at which a sender can transmit information over a noisy quantum channel. More often than not, the known formulas expressing these transmission rates are intractable, requiring an optimization over an infinite number of uses of the channel. Researchers have rarely found quantum channels with a tractable classical or quantum capacity, but when such a finding occurs, it demonstrates a complete understanding of that channel's capabilities for transmitting classical or quantum information. Here, we show that the three-dimensional capacity region for entanglement-assisted transmission of classical and quantum information is tractable for the Hadamard class of channels. Examples of Hadamard channels include generalized dephasing channels, cloning channels, and the Unruh channel. The generalized dephasing channels and the cloning channels are natural processes that occur in quantum systems through the loss of quantum coherence or stimulated emission, respectively. The Unruh channel is a noisy process that occurs in relativistic quantum information theory as a result of the Unruh effect and bears a strong relationship to the cloning channels. We give exact formulas for the entanglement-assisted classical and quantum communication capacity regions of these channels. The coding strategy for each of these examples is superior to a naive time-sharing strategy, and we introduce a measure to determine this improvement.Comment: 27 pages, 6 figures, some slight refinements and submitted to Physical Review

Identifying the quantum correlations in light-harvesting complexes

One of the major efforts in the quantum biological program is to subject biological systems to standard tests or measures of quantumness. These tests and measures should elucidate if non-trivial quantum effects may be present in biological systems. Two such measures of quantum correlations are the quantum discord and the relative entropy of entanglement. Here, we show that the relative entropy of entanglement admits a simple analytic form when dynamics and accessible degrees of freedom are restricted to a zero- and single-excitation subspace. We also simulate and calculate the amount of quantum discord that is present in the Fenna-Matthews-Olson protein complex during the transfer of an excitation from a chlorosome antenna to a reaction center. We find that the single-excitation quantum discord and relative entropy of entanglement are equal for all of our numerical simulations, but a proof of their general equality for this setting evades us for now. Also, some of our simulations demonstrate that the relative entropy of entanglement without the single-excitation restriction is much lower than the quantum discord. The first picosecond of dynamics is the relevant timescale for the transfer of the excitation, according to some sources in the literature. Our simulation results indicate that quantum correlations contribute a significant fraction of the total correlation during this first picosecond in many cases, at both cryogenic and physiological temperature.Comment: 15 pages, 7 figures, significant improvements including (1) an analytical formula for the single-excitation relative entropy of entanglement (REE), (2) simulations indicating that the single-excitation REE is equal to the single-excitation discord, and (3) simulations indicating that the full REE can be much lower than the single-excitation RE

Geometric measure of quantum discord and the geometry of a class of two-qubit states

We investigate the geometric picture of the level surfaces of quantum entanglement and geometric measure of quantum discord (GMQD) of a class of X-states, respectively. This pictorial approach provides us a direct understanding of the structure of entanglement and GMQD. The dynamic evolution of GMQD under two typical kinds of quantum decoherence channels is also investigated. It is shown that there exists a class of initial states for which the GMQD is not destroyed by decoherence in a finite time interval. Furthermore, we establish a factorization law between the initial and final GMQD, which allows us to infer the evolution of entanglement under the influences of the environment.Comment: 10 pages, 4 figures, comments are welcom

Lorentz-covariant, unitary evolution of a relativistic Majorana qubit

We formulate a covariant description of a relativistic qubit identified with an irreducible set of quantum spin states of a Majorana particle with a sharp momentum. We treat the particle’s four-momentum as an external parameter. We show that it is possible to define an interesting time evolution of the spin density matrix of such a qubit. This evolution is manifestly Lorentz covariant in the bispinor representation and unitary in the spin representation. Moreover, during this evolution the Majorana particle undergoes an uniformly accelerated motion. We classify possible types of such motions, and finally we illustrate the behaviour of the polarization vector of the Majorana qubit during the evolution in some special cases

Reconstructing the nonadaptive radiation of an ancient lineage of ground‐dwelling stick insects (Phasmatodea: Heteropterygidae)

Stick and leaf insects (Phasmatodea) are large terrestrial herbivorous arthropods known for masquerading as plant parts such as bark, twigs and leaves. Their evolutionary history is largely shaped by convergent evolution associated with adaptive radiations on geographically isolated landmasses that have repeatedly generated ground-dwelling ecomorphs. The members of one lineage, however, the Oriental Heteropterygidae, are morphologically rather uniform, and have a predominantly ground-dwelling lifestyle. The phylogeny of Heteropterygidae that comprises approximately 130 described species is controversial and remains uncertain. In particular, the systematic position of the giant Jungle Nymph Heteropteryx dilatata, whose males are capable of flight and exhibit the most plesiomorphic wing morphology among extant phasmatodeans, is of major interest to the scientific community. Here, we analysed a set of seven nuclear and mitochondrial genes to infer the phylogeny of Heteropterygidae covering the group's overall diversity. The divergence time estimation and reconstruction of the historical biogeography resulted in an ancestral distribution across Sundaland with long distance dispersal events to Wallacea, the Philippines and the South Pacific. We were able to resolve the relationships among the three principal subgroups of Heteropterygidae and revealed the Dataminae, which contain entirely wingless small forms, as the sister group of Heteropteryginae + Obriminae. Within Heteropteryginae, Haaniella is recovered as paraphyletic in regard to Heteropteryx. Consequently, Heteropteryx must be considered a subordinate taxon deeply embedded within a flightless clade of stick insects. Within Obriminae, the Bornean Hoploclonia is strongly supported as the earliest diverging lineage. Based on this finding, we recognize only two tribes of equal rank among Obriminae, the Hoplocloniini trib. nov. and Obrimini sensu nov. Within the latter, we demonstrate that previous tribal assignments do not reflect phylogenetic relationships and that a basal splitting event occurred between the wing-bearing clade Miroceramia + Pterobrimus and the remaining wingless Obrimini. The Philippine genus Tisamenus is paraphyletic with regard to Ilocano hebardi, thus, we transfer the latter species to Tisamenus as Tisamenus hebardi comb. nov. and synonymize Ilocano with Tisamenus. We discuss character transformations in the light of the new phylogenetic results and conclude that the current taxonomic diversity appears to be mainly driven by allopatry and not to be the result of niche differentiation. This radiation is thus best described as a nonadaptive radiation

Functional Subsystems and Quantum Redundancy in Photosynthetic Light Harvesting

The Fenna-Matthews-Olson (FMO) antennae complex, responsible for light harvesting in green sulfur bacteria, consists of three monomers, each with seven chromophores. Here we show that multiple subsystems of the seven chromophores can transfer energy from either chromophore 1 or 6 to the reaction center with an efficiency matching or in many cases exceeding that of the full seven chromophore system. In the FMO complex these functional subsystems support multiple quantum pathways for efficient energy transfer that provide a built-in quantum redundancy. There are many instances of redundancy in nature, providing reliability and protection, and in photosynthetic light harvesting this quantum redundancy provides protection against the temporary or permanent loss of one or more chromophores. The complete characterization of functional subsystems within the FMO complex offers a detailed map of the energy flow within the FMO complex, which has potential applications to the design of more efficient photovoltaic devices