Simple Proof of Security of the BB84 Quantum Key Distribution Protocol

We prove the security of the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution. We first give a key distribution protocol based on entanglement purification, which can be proven secure using methods from Lo and Chau's proof of security for a similar protocol. We then show that the security of this protocol implies the security of BB84. The entanglement-purification based protocol uses Calderbank-Shor-Steane (CSS) codes, and properties of these codes are used to remove the use of quantum computation from the Lo-Chau protocol.Comment: 5 pages, Latex, minor changes to improve clarity and fix typo

Factors Associated with Maternal Wellbeing at Four Months Post-Partum in Ireland

This study aimed to examine factors associated with maternal wellbeing at four months post-partum in the Irish context. Socio-demographic, health behaviour and infant feeding data were collected in pregnancy, at birth and at 17 weeks post-partum. Maternal distress, body image and resilience were measured at 17 weeks post-partum. Binary logistic regression predicted maternal distress and statistical significance was taken at p \u3c 0.05. One hundred and seventy-two women were followed-up in pregnancy, at birth and at 17 weeks post-partum. Three in five (61.6%, n106) initiated breastfeeding. At 17 weeks post-partum, 23.8% (n41) were exclusively or partially breastfeeding and over a third (36.0%, n62) of all mothers were at risk of distress. In multivariate analyses, independent predictors of distress included: low maternal resilience (p \u3c 0.01, odds ratio (OR): 7.22 (95% confidence interval [CI]: 2.49–20.95)); unsatisfactory partner support (p = 0.02, OR: 3.89 (95% CI: 1.20–12.65)); older age (p = 0.02, OR: 1.11 (95% CI: 1.02–1.21)); and breastfeeding (p = 0.01, OR: 2.89 (95% CI: 1.29–6.47)). Routine assessment of emotional wellbeing and targeted interventions are needed to promote a more healthful transition to motherhood among women in Ireland

Can non-private channels transmit quantum information?

We study the power of quantum channels with little or no capacity for private communication. Because privacy is a necessary condition for quantum communication, one might expect that such channels would be of little use for transmitting quantum states. Nevertheless, we find strong evidence that there are pairs of such channels that, when used together, can transmit far more quantum information than the sum of their individual private capacities. Because quantum transmissions are necessarily private, this would imply a large violation of additivity for the private capacity. Specifically, we present channels which display either (1) A large joint quantum capacity but very small individual private capacities or (2) a severe violation of additivity for the Holevo information.Comment: We both think so. 4 pages and 3 figures explain wh

Secure quantum key distribution with an uncharacterized source

We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol for an arbitrary source whose averaged states are basis-independent, a condition that is automatically satisfied if the source is suitably designed. The proof is based on the observation that, to an adversary, the key extraction process is equivalent to a measurement in the sigma_x-basis performed on a pure sigma_z-basis eigenstate. The dependence of the achievable key length on the bit error rate is the same as that established by Shor and Preskill for a perfect source, indicating that the defects in the source are efficiently detected by the protocol.Comment: 4 pages, 1 figure, REVTeX, minor revision

The Parity Bit in Quantum Cryptography

An $n$-bit string is encoded as a sequence of non-orthogonal quantum states. The parity bit of that $n$-bit string is described by one of two density matrices, $\rho_0^{(n)}$ and $\rho_1^{(n)}$, both in a Hilbert space of dimension $2^n$. In order to derive the parity bit the receiver must distinguish between the two density matrices, e.g., in terms of optimal mutual information. In this paper we find the measurement which provides the optimal mutual information about the parity bit and calculate that information. We prove that this information decreases exponentially with the length of the string in the case where the single bit states are almost fully overlapping. We believe this result will be useful in proving the ultimate security of quantum crytography in the presence of noise.Comment: 19 pages, RevTe

Hybrid vertex-midline modelling of elongated plant organs

We describe a method for the simulation of the growth of elongated plant organs, such as seedling roots. By combining a midline representation of the organ on a tissue scale and a vertex-based representation on the cell scale, we obtain a multiscale method, which is able to both simulate organ growth and incorporate cell-scale processes. Equations for the evolution of the midline are obtained, which depend on the cell-wall properties of individual cells through appropriate averages over the vertex-based representation. The evolution of the organ midline is used to deform the cellular-scale representation. This permits the investigation of the regulation of organ growth through the cell-scale transport of the plant hormone auxin. The utility of this method is demonstrated in simulating the early stages of the response of a root to gravity, using a vertex-based template acquired from confocal imaging. Asymmetries in the concentrations of auxin between the upper and lower sides of the root lead to bending of the root midline, reflecting a gravitropic response

Maximum Power Efficiency and Criticality in Random Boolean Networks

Random Boolean networks are models of disordered causal systems that can occur in cells and the biosphere. These are open thermodynamic systems exhibiting a flow of energy that is dissipated at a finite rate. Life does work to acquire more energy, then uses the available energy it has gained to perform more work. It is plausible that natural selection has optimized many biological systems for power efficiency: useful power generated per unit fuel. In this letter we begin to investigate these questions for random Boolean networks using Landauer's erasure principle, which defines a minimum entropy cost for bit erasure. We show that critical Boolean networks maximize available power efficiency, which requires that the system have a finite displacement from equilibrium. Our initial results may extend to more realistic models for cells and ecosystems.Comment: 4 pages RevTeX, 1 figure in .eps format. Comments welcome, v2: minor clarifications added, conclusions unchanged. v3: paper rewritten to clarify it; conclusions unchange

The Submillimeter Polarization Spectrum of M17

We present 450 {\mu}m polarimetric observations of the M17 molecular cloud obtained with the SHARP polarimeter at the Caltech Submillimeter Observatory. Across the observed region, the magnetic field orientation is consistent with previous submillimeter and far-infrared polarization measurements. Our observations are centered on a region of the molecular cloud that has been compressed by stellar winds from a cluster of OB stars. We have compared these new data with previous 350 {\mu}m polarimetry and find an anti-correlation between the 450 to 350 {\mu}m polarization magnitude ratio and the ratio of 21 cm to 450 {\mu}m intensity. The polarization ratio is lower near the east end of the studied region where the cloud is exposed to stellar winds and radiation. At the west end of the region, the polarization ratio is higher. We interpret the varying polarization spectrum as evidence supporting the radiative alignment torque (RAT) model for grain alignment, implying higher alignment efficiency in the region that is exposed to a higher anisotropic radiation field.Comment: 24 pages, 10 figure