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

Closed form expressions for crack mouth displacements and stress intensity factors for chevron notched short bar and short rod specimens based on experimental compliance measurements

A set of equations are presented describing certain fracture mechanics parameters for chevron notch bar and rod specimens. They are developed by fitting compliance calibration data reported earlier. The equations present the various parameters in their most useful forms. The data encompass the entire range of the specimen geometries most commonly used. Their use will facilitate the testing and analysis of brittle metals, ceramics, and glasses

Configurational entropy of network-forming materials

We present a computationally efficient method to calculate the configurational entropy of network-forming materials. The method requires only the atomic coordinates and bonds of a single well-relaxed configuration. This is in contrast to the multiple simulations that are required for other methods to determine entropy, such as thermodynamic integration. We use our method to obtain the configurational entropy of well-relaxed networks of amorphous silicon and vitreous silica. For these materials we find configurational entropies of 1.02 kb and 0.97 kb per silicon atom, respectively, with kb the Boltzmann constant.Comment: 4 pages, 4 figure

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

Fracture toughness of brittle materials determined with chevron notch specimens

The use of chevron-notch specimens for determining the plane strain fracture toughness (K sub Ic) of brittle materials is discussed. Three chevron-notch specimens were investigated: short bar, short rod, and four-point-bend. The dimensionless stress intensity coefficient used in computing K sub Ic is derived for the short bar specimen from the superposition of ligament-dependent and ligament-independent solutions for the straight through crack, and also from experimental compliance calibrations. Coefficients for the four-point-bend specimen were developed by the same superposition procedure, and with additional refinement using the slice model of Bluhm. Short rod specimen stress intensity coefficients were determined only by experimental compliance calibration. Performance of the three chevron-notch specimens and their stress intensity factor relations were evaluated by tests on hot-pressed silicon nitride and sintered aluminum oxide. Results obtained with the short bar and the four-point-bend specimens on silicon nitride are in good agreement and relatively free of specimen geometry and size effects within the range investigated. Results on aluminum oxide were affected by specimen size and chevron-notch geometry, believed due to a rising crack growth resistance curve for the material. Only the results for the short bar specimen are presented in detail

Very long baseline astrometry of PSR J1012+5307 and its implications on alternative theories of gravity

PSR J1012+5307, a millisecond pulsar in orbit with a helium white dwarf (WD), has been timed with high precision for about 25 years. One of the main objectives of this long-term timing is to use the large asymmetry in gravitational binding energy between the neutron star and the WD to test gravitational theories. Such tests, however, will be eventually limited by the accuracy of the distance to the pulsar. Here, we present VLBI (very long baseline interferometry) astrometry results spanning approximately 2.5 years for PSR J1012+5307, obtained with the Very Long Baseline Array as part of the MSPSRPI project. These provide the first proper motion and absolute position for PSR J1012+5307 measured in a quasi-inertial reference frame. From the VLBI results, we measure a distance of $0.83^{+0.06}_{-0.02}$kpc (all the estimates presented in the abstract are at 68% confidence) for PSR J1012+5307, which is the most precise obtained to date. Using the new distance, we improve the uncertainty of measurements of the unmodeled contributions to orbital period decay, which, combined with three other pulsars, places new constraints on the coupling constant for dipole gravitational radiation $\kappa_D=(-1.7\pm1.7)\times 10^{-4}$ and the fractional time derivative of Newton's gravitational constant $\dot{G}/G = -1.8^{\,+5.6}_{\,-4.7}\times 10^{-13}\,{\rm yr^{-1}}$ in the local universe. As the uncertainties of the observed decays of orbital period for the four leading pulsar-WD systems become negligible in $\approx10$ years, the uncertainties for $\dot{G}/G$ and $\kappa_D$ will be improved to $\leq1.5\times10^{-13}\,{\rm yr^{-1}}$ and $\leq1.0\times10^{-4}$, respectively, predominantly limited by the distance uncertainties.Comment: published in ApJ (2020ApJ...896...85D

Statistical mechanics of lossy compression for non-monotonic multilayer perceptrons

A lossy data compression scheme for uniformly biased Boolean messages is investigated via statistical mechanics techniques. We utilize tree-like committee machine (committee tree) and tree-like parity machine (parity tree) whose transfer functions are non-monotonic. The scheme performance at the infinite code length limit is analyzed using the replica method. Both committee and parity treelike networks are shown to saturate the Shannon bound. The AT stability of the Replica Symmetric solution is analyzed, and the tuning of the non-monotonic transfer function is also discussed.Comment: 29 pages, 7 figure

Analysis of some compliance calibration data for chevron-notch bar and rod specimens

A set of equations describing certain fracture mechanics parameters for chevron-notch bar and rod specimens are presented. They are developed by fitting earlier compliance calibration data. The difficulty in determining the minimum stress intensity coefficient and the critical crack length is discussed

Statistical mechanics of lossy data compression using a non-monotonic perceptron

The performance of a lossy data compression scheme for uniformly biased Boolean messages is investigated via methods of statistical mechanics. Inspired by a formal similarity to the storage capacity problem in the research of neural networks, we utilize a perceptron of which the transfer function is appropriately designed in order to compress and decode the messages. Employing the replica method, we analytically show that our scheme can achieve the optimal performance known in the framework of lossy compression in most cases when the code length becomes infinity. The validity of the obtained results is numerically confirmed.Comment: 9 pages, 5 figures, Physical Review