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

Entanglement can completely defeat quantum noise

We describe two quantum channels that individually cannot send any information, even classical, without some chance of decoding error. But together a single use of each channel can send quantum information perfectly reliably. This proves that the zero-error classical capacity exhibits superactivation, the extreme form of the superadditivity phenomenon in which entangled inputs allow communication over zero capacity channels. But our result is stronger still, as it even allows zero-error quantum communication when the two channels are combined. Thus our result shows a new remarkable way in which entanglement across two systems can be used to resist noise, in this case perfectly. We also show a new form of superactivation by entanglement shared between sender and receiver.Comment: 4 pages, 1 figur

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

Measuring the effective complexity of cosmological models

We introduce a statistical measure of the effective model complexity, called the Bayesian complexity. We demonstrate that the Bayesian complexity can be used to assess how many effective parameters a set of data can support and that it is a useful complement to the model likelihood (the evidence) in model selection questions. We apply this approach to recent measurements of cosmic microwave background anisotropies combined with the Hubble Space Telescope measurement of the Hubble parameter. Using mildly non-informative priors, we show how the 3-year WMAP data improves on the first-year data by being able to measure both the spectral index and the reionization epoch at the same time. We also find that a non-zero curvature is strongly disfavored. We conclude that although current data could constrain at least seven effective parameters, only six of them are required in a scheme based on the Lambda-CDM concordance cosmology.Comment: 9 pages, 4 figures, revised version accepted for publication in PRD, updated with WMAP3 result

Structured optical receivers to attain superadditive capacity and the Holevo limit

When classical information is sent over a quantum channel, attaining the ultimate limit to channel capacity requires the receiver to make joint measurements over long codeword blocks. For a pure-state channel, we construct a receiver that can attain the ultimate capacity by applying a single-shot unitary transformation on the received quantum codeword followed by simultaneous (but separable) projective measurements on the single-modulation-symbol state spaces. We study the ultimate limits of photon-information-efficient communications on a lossy bosonic channel. Based on our general results for the pure-state quantum channel, we show some of the first concrete examples of codes and structured joint-detection optical receivers that can achieve fundamentally higher (superadditive) channel capacity than conventional receivers that detect each modulation symbol individually.Comment: 4 pages, 4 figure

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

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