Quantum Entanglement Capacity with Classical Feedback

For any quantum discrete memoryless channel, we define a quantity called quantum entanglement capacity with classical feedback ($E_B$), and we show that this quantity lies between two other well-studied quantities. These two quantities - namely the quantum capacity assisted by two-way classical communication ($Q_2$) and the quantum capacity with classical feedback ($Q_B$) - are widely conjectured to be different: there exists quantum discrete memoryless channel for which $Q_2>Q_B$. We then present a general scheme to convert any quantum error-correcting codes into adaptive protocols for this newly-defined quantity of the quantum depolarizing channel, and illustrate with Cat (repetition) code and Shor code. We contrast the present notion with entanglement purification protocols by showing that whilst the Leung-Shor protocol can be applied directly, recurrence methods need to be supplemented with other techniques but at the same time offer a way to improve the aforementioned Cat code. For the quantum depolarizing channel, we prove a formula that gives lower bounds on the quantum capacity with classical feedback from any $E_B$ protocols. We then apply this formula to the $E_B$ protocols that we discuss to obtain new lower bounds on the quantum capacity with classical feedback of the quantum depolarizing channel

Statistical mechanics of lossy compression using multilayer perceptrons

Statistical mechanics is applied to lossy compression using multilayer perceptrons for unbiased Boolean messages. We utilize a tree-like committee machine (committee tree) and tree-like parity machine (parity tree) whose transfer functions are monotonic. For compression using committee tree, a lower bound of achievable distortion becomes small as the number of hidden units K increases. However, it cannot reach the Shannon bound even where K -> infty. For a compression using a parity tree with K >= 2 hidden units, the rate distortion function, which is known as the theoretical limit for compression, is derived where the code length becomes infinity.Comment: 12 pages, 5 figure

Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series

A nonlinear dynamics approach can be used in order to quantify complexity in written texts. As a first step, a one-dimensional system is examined : two written texts by one author (Lewis Carroll) are considered, together with one translation, into an artificial language, i.e. Esperanto are mapped into time series. Their corresponding shuffled versions are used for obtaining a "base line". Two different one-dimensional time series are used here: (i) one based on word lengths (LTS), (ii) the other on word frequencies (FTS). It is shown that the generalized Hurst exponent $h(q)$ and the derived $f(\alpha)$ curves of the original and translated texts show marked differences. The original "texts" are far from giving a parabolic $f(\alpha)$ function, - in contrast to the shuffled texts. Moreover, the Esperanto text has more extreme values. This suggests cascade model-like, with multiscale time asymmetric features as finally written texts. A discussion of the difference and complementarity of mapping into a LTS or FTS is presented. The FTS $f(\alpha)$ curves are more opened than the LTS onesComment: preprint for PRE; 2 columns; 10 pages; 6 (multifigures); 3 Tables; 70 reference

LOGISTICAL COSTS AND RISKS OF MARKETING GENETICALLY MODIFIED WHEAT

Genetically modified (GM) grains have increased in importance. Moving biotech grains from producers to processors is a challenge for the grain handling system that could involve increased segregations. The objective of this research is to determine how testing strategies affect the logistical costs of a grain pipeline when GM wheat is present. A logistical model was developed and simulated to analyze impacts of uncertainty in demand, receipts, test accuracy, rail deliveries, and transit time. Sensitivities were conducted on certain variables to determine their effects on logistical costs. Analysis revealed that logistical costs are impacted by the number of quality categories and uncertainties in the system. Adding GM grains increased costs due to testing requirements and increased segregation demands as the number of wheat categories rises.Genetically Modified (GM) Grains, Logistical Costs, Testing, Risk, Segregation, Crop Production/Industries, Research and Development/Tech Change/Emerging Technologies,

LOGISTICAL COSTS AND STRATEGIES FOR WHEAT SEGREGATION

Special segregations that provide unique qualities for end use products are being specified by buyers. As users of wheat become more specific about quality, the number of quality segregations that the logistical pipeline must accommodate increases. The additional cost of increased grain segregations will influence the optimal level of wheat variety segregations marketed in a supply chain. The primary objective of this research is to develop a model that captures the logistical costs of increased grain segregations in the marketing system. A simulation model was developed to add logistical uncertainty in demand, receipts, rail deliveries, and transit time. Sensitivities were conducted on certain variables to determine their effects on logistical costs. Logistical costs increase as more segregations are added. In addition, increasing uncertainty into the system raises logistical costs. Pipeline configuration also affects costs as the number of categories/storage bins present at origin may differ from the wheat categories demanded or the number of storage bins present at the export elevator.wheat, segregations, Crop Production/Industries,

Quantum Entanglement of Moving Bodies

We study the properties of quantum information and quantum entanglement in moving frames. We show that the entanglement between the spins and the momenta of two particles can be interchanged under a Lorentz transformation, so that a pair of particles that is entangled in spin but not momentum in one reference frame, may, in another frame, be entangled in momentum at the expense of spin-entanglement. Similarly, entanglement between momenta may be transferred to spin under a Lorentz transformation. While spin and momentum entanglement each is not Lorentz invariant, the joint entanglement of the wave function is.Comment: 4 pages, 2 figures. An error was corrected in the numerical data and hence the discussion of the data was changed. Also, references were added. Another example was added to the pape

Quantum Capacity Approaching Codes for the Detected-Jump Channel

The quantum channel capacity gives the ultimate limit for the rate at which quantum data can be reliably transmitted through a noisy quantum channel. Degradable quantum channels are among the few channels whose quantum capacities are known. Given the quantum capacity of a degradable channel, it remains challenging to find a practical coding scheme which approaches capacity. Here we discuss code designs for the detected-jump channel, a degradable channel with practical relevance describing the physics of spontaneous decay of atoms with detected photon emission. We show that this channel can be used to simulate a binary classical channel with both erasures and bit-flips. The capacity of the simulated classical channel gives a lower bound on the quantum capacity of the detected-jump channel. When the jump probability is small, it almost equals the quantum capacity. Hence using a classical capacity approaching code for the simulated classical channel yields a quantum code which approaches the quantum capacity of the detected-jump channel