Avoiding Irreversibility: Engineering Resonant Conversions of Quantum Resources

© 2019 American Physical Society. We identify and explore the intriguing property of resource resonance arising within resource theories of entanglement, coherence, and thermodynamics. While the theories considered are reversible asymptotically, the same is generally not true in realistic scenarios where the available resources are bounded. The finite-size effects responsible for this irreversibility could potentially prohibit small quantum information processors or thermal machines from achieving their full potential. Nevertheless, we show here that by carefully engineering the resource interconversion process any such losses can be greatly suppressed. Our results are predicted by higher order expansions of the trade-off between the rate of resource interconversion and the achieved fidelity, and are verified by exact numerical optimizations of the appropriate underlying approximate majorization conditions

Moderate Deviation Analysis for Classical Communication over Quantum Channels

© 2017, Springer-Verlag GmbH Germany. We analyse families of codes for classical data transmission over quantum channels that have both a vanishing probability of error and a code rate approaching capacity as the code length increases. To characterise the fundamental tradeoff between decoding error, code rate and code length for such codes we introduce a quantum generalisation of the moderate deviation analysis proposed by Altŭg and Wagner as well as Polyanskiy and Verdú. We derive such a tradeoff for classical-quantum (as well as image-additive) channels in terms of the channel capacity and the channel dispersion, giving further evidence that the latter quantity characterises the necessary backoff from capacity when transmitting finite blocks of classical data. To derive these results we also study asymmetric binary quantum hypothesis testing in the moderate deviations regime. Due to the central importance of the latter task, we expect that our techniques will find further applications in the analysis of other quantum information processing tasks

Beyond the thermodynamic limit: Finite-size corrections to state interconversion rates

Thermodynamics is traditionally constrained to the study of macroscopic systems whose energy fluctuations are negligible compared to their average energy. Here, we push beyond this thermodynamic limit by developing a mathematical framework to rigorously address the problem of thermodynamic transformations of finite-size systems. More formally, we analyse state interconversion under thermal operations and between arbitrary energy-incoherent states. We find precise relations between the optimal rate at which interconversion can take place and the desired infidelity of the final state when the system size is sufficiently large. These so-called second-order asymptotics provide a bridge between the extreme cases of single-shot thermodynamics and the asymptotic limit of infinitely large systems. We illustrate the utility of our results with several examples. We first show how thermodynamic cycles are affected by irreversibility due to finite-size effects. We then provide a precise expression for the gap between the distillable work and work of formation that opens away from the thermodynamic limit. Finally, we explain how the performance of a heat engine gets affected when the working body is small. We find that while perfect work cannot generally be extracted at Carnot efficiency, there are conditions under which these finite-size effects vanish. In deriving our results we also clarify relations between different notions of approximate majorisation

AID-Targeting and Hypermutation of Non-Immunoglobulin Genes Does Not Correlate with Proximity to Immunoglobulin Genes in Germinal Center B Cells

Upon activation, B cells divide, form a germinal center, and express the activation induced deaminase (AID), an enzyme that triggers somatic hypermutation of the variable regions of immunoglobulin (Ig) loci. Recent evidence indicates that at least 25% of expressed genes in germinal center B cells are mutated or deaminated by AID. One of the most deaminated genes, c-Myc, frequently appears as a translocation partner with the Ig heavy chain gene (Igh) in mouse plasmacytomas and human Burkitt's lymphomas. This indicates that the two genes or their double-strand break ends come into close proximity at a biologically relevant frequency. However, the proximity of c-Myc and Igh has never been measured in germinal center B cells, where many such translocations are thought to occur. We hypothesized that in germinal center B cells, not only is c-Myc near Igh, but other mutating non-Ig genes are deaminated by AID because they are near Ig genes, the primary targets of AID. We tested this “collateral damage” model using 3D-fluorescence in situ hybridization (3D-FISH) to measure the distance from non-Ig genes to Ig genes in germinal center B cells. We also made mice transgenic for human MYC and measured expression and mutation of the transgenes. We found that there is no correlation between proximity to Ig genes and levels of AID targeting or gene mutation, and that c-Myc was not closer to Igh than were other non-Ig genes. In addition, the human MYC transgenes did not accumulate mutations and were not deaminated by AID. We conclude that proximity to Ig loci is unlikely to be a major determinant of AID targeting or mutation of non-Ig genes, and that the MYC transgenes are either missing important regulatory elements that allow mutation or are unable to mutate because their new nuclear position is not conducive to AID deamination

Moderate deviation analysis of majorisation-based resource interconversion

© 2019 IEEE. We consider the problem of interconverting a finite amount of resources within all theories whose single-shot transformation rules are based on a majorisation relation, e.g. the resource theories of entanglement and coherence (for pure state transformations), as well as thermodynamics (for energy-incoherent transformations). When only finite resources are available we expect to see a non-trivial trade-off between the rate rn at which n copies of a resource state ρ can be transformed into nrn copies of another resource state σ, and the error level ϵn of the interconversion process, as a function of n. In this work we derive the optimal trade-off in the so-called moderate deviation regime, where the rate of interconversion rn approaches its optimum in the asymptotic limit of unbounded resources (n → ∞), while the error ϵn vanishes in the same limit. We find that the moderate deviation analysis exhibits a resonance behaviour which implies that certain pairs of resource states can be interconverted at the asymptotically optimal rate with negligible error, even in the finite n regime

Spatial and temporal changes in egg production in the western rock lobster (Panulirus cygnus) fishery

Size at maturity in the western rock lobster (Panulirus cygnus) fishery in Australia increases from north to south and female lobsters carry either one or two batches of eggs per season depending on their carapace length. There has been a steady decrease in the size at first maturity of western rock lobster over the last 30 years, and there are now significantly more small females, many below the legal minimum size, contributing to the brood stock than any time since the fishery has been researched. Biological data were used to show the current contribution to egg production in different management regions of the fishery and historical length-frequency data were used to show how egg production has changed in those regions overtime. Reasons for the change in size at maturity in this fishery are unclear, but the outcome has been that egg production is now more evenly distributed across management zones. Egg production was high at Abrolhos Islands in the 1990s owing to strong year classes of breeding animals entering the fishery over those years. In the period since 2000, egg production has fallen sharply at the islands, but has increased in the coastal population compared with the 1980s and 1990s