Entangled states maximize the two qubit channel capacity for some Pauli channels with memory

We prove that a general upper bound on the maximal mutual information of quantum channels is saturated in the case of Pauli channels with an arbitrary degree of memory. For a subset of such channels we explicitly identify the optimal signal states. We show analytically that for such a class of channels entangled states are indeed optimal above a given memory threshold. It is noteworthy that the resulting channel capacity is a non-differentiable function of the memory parameter.Comment: 4 pages no figure

Low temperature thermodynamics of charged bosons in a random potential and the specific heat of La_{2-x}Sr_{x}CuO_{4} below Tc

We propose a simple analytical form of the partition function for charged bosons localised in a random potential and derive the consequent thermodynamics below the superfluid transition temperature. In the low temperature limit, the specific heat, C, depends on the localisation length exponent nu: C is linear for nu1 we find C proportional to T^{1/nu}. This unusual sub-linear temperature dependence of the specific heat has recently been observed in La_{2-x}Sr_{x}CuO_{4} below Tc.Comment: Revtex, 6 pages, 4 postscript figure

Multiplicativity of completely bounded p-norms implies a new additivity result

We prove additivity of the minimal conditional entropy associated with a quantum channel Phi, represented by a completely positive (CP), trace-preserving map, when the infimum of S(gamma_{12}) - S(gamma_1) is restricted to states of the form gamma_{12} = (I \ot Phi)(| psi >< psi |). We show that this follows from multiplicativity of the completely bounded norm of Phi considered as a map from L_1 -> L_p for L_p spaces defined by the Schatten p-norm on matrices; we also give an independent proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L_1 -> L_p norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.Comment: Final version for Commun. Math. Physics. Section 5.2 of previous version deleted in view of the results in quant-ph/0601071 Other changes mino

Comments on Hastings' Additivity Counterexamples

Hastings recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy. In this paper we present an expanded version of Hastings' proof. In addition to a careful elucidation of the details of the proof, we also present bounds for the minimal dimensions needed to obtain a counterexample.Comment: 38 page

Classification in sparse, high dimensional environments applied to distributed systems failure prediction

Network failures are still one of the main causes of distributed systems’ lack of reliability. To overcome this problem we present an improvement over a failure prediction system, based on Elastic Net Logistic Regression and the application of rare events prediction techniques, able to work with sparse, high dimensional datasets. Specifically, we prove its stability, fine tune its hyperparameter and improve its industrial utility by showing that, with a slight change in dataset creation, it can also predict the location of a failure, a key asset when trying to take a proactive approach to failure management

Immunosuppression in Autoimmune Hepatitis: Is There an End Game?

Autoimmune hepatitis (AIH) is a rare, chronic disease associated with the development of cirrhosis and premature mortality. Current guidelines state that patients with AIH should receive induction therapy with corticosteroids or the combination of corticosteroids/azathioprine, followed by maintenance therapy with lower doses of steroids and/or azathioprine (1–3). However, the optimal strategy for the ongoing treatment beyond this point remains unclear

Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0

Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Renyi entropies of channels are not generally additive for p>1, we demonstrate here by a careful random selection argument that also at p=0, and consequently for sufficiently small p, there exist counterexamples. An explicit construction of two channels from 4 to 3 dimensions is given, which have non-multiplicative minimum output rank; for this pair of channels, numerics strongly suggest that the p-Renyi entropy is non-additive for all p < 0.11. We conjecture however that violations of additivity exist for all p<1.Comment: 7 pages, revtex4; v2 added correct ref. [15]; v3 has more information on the numerical violation as well as 1 figure (2 graphs) - note that the explicit example was changed and the more conservative estimate of the bound up to which violations occur, additionally some other small issues are straightened ou

The quantum dynamic capacity formula of a quantum channel

The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon theory literature. In this work, we prove the theorem with an "ab initio" approach, using only the most basic tools in the quantum information theorist's toolkit: the Alicki-Fannes' inequality, the chain rule for quantum mutual information, elementary properties of quantum entropy, and the quantum data processing inequality. The result is a simplified proof of the theorem that should be more accessible to those unfamiliar with the quantum Shannon theory literature. We also demonstrate that the "quantum dynamic capacity formula" characterizes the Pareto optimal trade-off surface for the full dynamic capacity region. Additivity of this formula simplifies the computation of the trade-off surface, and we prove that its additivity holds for the quantum Hadamard channels and the quantum erasure channel. We then determine exact expressions for and plot the dynamic capacity region of the quantum dephasing channel, an example from the Hadamard class, and the quantum erasure channel.Comment: 24 pages, 3 figures; v2 has improved structure and minor corrections; v3 has correction regarding the optimizatio

Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1

For all p > 1, we demonstrate the existence of quantum channels with non-multiplicative maximal output p-norms. Equivalently, for all p >1, the minimum output Renyi entropy of order p of a quantum channel is not additive. The violations found are large; in all cases, the minimum output Renyi entropy of order p for a product channel need not be significantly greater than the minimum output entropy of its individual factors. Since p=1 corresponds to the von Neumann entropy, these counterexamples demonstrate that if the additivity conjecture of quantum information theory is true, it cannot be proved as a consequence of any channel-independent guarantee of maximal p-norm multiplicativity. We also show that a class of channels previously studied in the context of approximate encryption lead to counterexamples for all p > 2.Comment: Merger of arXiv:0707.0402 and arXiv:0707.3291 containing new and improved analysis of counterexamples. 17 page

Epistemic and social scripts in computer-supported collaborative learning

Collaborative learning in computer-supported learning environments typically means that learners work on tasks together, discussing their individual perspectives via text-based media or videoconferencing, and consequently acquire knowledge. Collaborative learning, however, is often sub-optimal with respect to how learners work on the concepts that are supposed to be learned and how learners interact with each other. One possibility to improve collaborative learning environments is to conceptualize epistemic scripts, which specify how learners work on a given task, and social scripts, which structure how learners interact with each other. In this contribution, two studies will be reported that investigated the effects of epistemic and social scripts in a text-based computer-supported learning environment and in a videoconferencing learning environment in order to foster the individual acquisition of knowledge. In each study the factors ‘epistemic script’ and ‘social script’ have been independently varied in a 2×2-factorial design. 182 university students of Educational Science participated in these two studies. Results of both studies show that social scripts can be substantially beneficial with respect to the individual acquisition of knowledge, whereas epistemic scripts apparently do not to lead to the expected effects