Efficiency of quantum energy teleportation within spin-$$\frac{1}{2}$$ particle pairs

A protocol for quantum energy teleportation (QET) is known for a so-called minimal spin-\(\frac{1}{2}\) particle pair model. We extend this protocol to explicitly admit quantum weak measurements at its first stage. The extended protocol is applied beyond the minimal model to spin-\(\frac{1}{2}\) particle pairs whose Hamiltonians are of a general class characterized by orthogonal pairs of entangled eigenstates. The energy transfer efficiency of the extended QET protocol is derived for this setting, and we show that weaker measurement yields greater efficiency. In the minimal particle pair model, for example, the efficiency can be doubled by this means. We also show that the QET protocol’s transfer efficiency never exceeds 100 %, supporting the understanding that quantum energy teleportation is, indeed, an energy transfer protocol, rather than a protocol for remotely catalyzing local extraction of system energy already present.     

New asymmetric quantum codes over $$F_{q}$$

Two families of new asymmetric quantum codes are constructed in this paper. The first family is the asymmetric quantum codes with length \(n=q^{m}-1\) over \(F_{q}\), where \(q\ge 5\) is a prime power. The second one is the asymmetric quantum codes with length \(n=3^{m}-1\). These asymmetric quantum codes are derived from the CSS construction and pairs of nested BCH codes. Moreover, let the defining set \(T_{1}=T_{2}^{-q}\), then the real Z-distance of our asymmetric quantum codes are much larger than \(\delta _\mathrm{max}+1\), where \(\delta _\mathrm{max}\) is the maximal designed distance of dual-containing narrow-sense BCH code, and the parameters presented here have better than the ones available in the literature.     

\frac{13}{9}-Approximation for Graphic TSP

The Travelling Salesman Problem is one of the fundamental and intensively studied problems in approximation algorithms. For more than 30 years, the best algorithm known for general metrics has been Christofides’s algorithm with an approximation factor of \(\frac{3}{2}\) , even though the so-called Held-Karp LP relaxation of the problem is conjectured to have the integrality gap of only \(\frac{4}{3}\) . Very recently, significant progress has been made for the important special case of graphic metrics, first by Oveis Gharan et al. (FOCS, 550–559, 2011), and then by Mömke and Svensson (FOCS, 560–569, 2011). In this paper, we provide an improved analysis of the approach presented in Mömke and Svensson (FOCS, 560–569, 2011) yielding a bound of \(\frac{13}{9}\) on the approximation factor, as well as a bound of \(\frac{19}{12}+\varepsilon\) for any ε>0 for a more general Travelling Salesman Path Problem in graphic metrics.     

Ordered fields and {{{\rm \L}\Pi\frac{1}{2}}} -algebras

In this work we further explore the connection between -algebras and ordered fields. We show that any two -chains generate the same variety if and only if they are related to ordered fields that have the same universal theory. This will yield that any -chain generates the whole variety if and only if it contains a subalgebra isomorphic to the -chain of real algebraic numbers, that consequently is the smallest -chain generating the whole variety. We also show that any two different subalgebras of the -chain over the real algebraic numbers generate different varieties. This will be exploited in order to prove that the lattice of subvarieties of -algebras has the cardinality of the continuum. Finally, we will also briefly deal with some model-theoretic properties of -chains related to real closed fields, proving quantifier-elimination and related results.     

Singular $$\mathcal{H}$$ 2-optimization problems for discrete-time systems

Singular ₂-optimization problems are considered for the standard discrete-time control system. Two types of singularity (type I and type II) are distinguished. A detailed treatment of problems with singularity of type II, which leads to nonuniqueness of solution, is presented. New algorithms for design of optimal controllers are presented both in frequency domain and state space, which generalize standard procedures onto the case of singular ₂-problems. A parameterization of the set of optimal controllers is given.Translated from Avtomatika i Telemekhanika, No. 3, 2005, pp. 20–33.Original Russian Text Copyright © 2005 by Polyakov.This paper was recommended for publication by B.T. Polyak, a member of the Editorial Board     

On Projection Matrices $$\mathcal{P}^k \to \mathcal{P}^2 ,k = 3,...,6, $$ and their Applications in Computer Vision

Projection matrices from projective spaces have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices (where k > 3) and methods for extracting the (non-rigid) structure and motion for each application.     

Experimental estimation of discord in an antiferromagnetic Heisenberg compound $$\hbox {Cu}(\hbox {NO}_{3})_{2}\cdot 2.5\,\hbox {H}_{2}\hbox {O}$$

Temperature-dependent static magnetic susceptibility and heat capacity data were employed to quantify quantum discord in copper nitrate \((\hbox {CN, Cu}(\hbox {NO}_{3})_{2}\cdot 2.5\, \hbox {H}_{2}\hbox {O})\) which is a spin 1/2 antiferromagnetic Heisenberg system. With the help of existing theoretical formulations, quantum discord, mutual information, and purely classical correlation were estimated as a function of temperature using the experimental data. The experimentally quantified correlations estimated from susceptibility and heat capacity data are consistent with each other, and they exhibit a good match with theoretical predictions. Violation of Bell’s inequality was also checked using the static magnetic susceptibility as well as heat capacity data. Quantum discord estimated from magnetic susceptibility as well as heat capacity data is found to be present in the thermal states of the system even when the system is in a separable state.     

Mutually unbiased special entangled bases with Schmidt number 2 in $${\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}$$

A way of constructing special entangled basis with fixed Schmidt number 2 (SEB2) in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k\in z^+,3\not \mid k)\) is proposed, and the conditions mutually unbiased SEB2s (MUSEB2s) satisfy are discussed. In addition, a very easy way of constructing MUSEB2s in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k=2^l)\) is presented. We first establish the concrete construction of SEB2 and MUSEB2s in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4}\) and \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{8}\), respectively, and then generalize them into \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k\in z^+,3\not \mid k)\) and display the condition that MUSEB2s satisfy; we also give general form of two MUSEB2s as examples in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k=2^l)\).     

Discrete p-robust $$\varvec{H}({{\mathrm{div}}})$$-liftings and a posteriori estimates for elli ptic problems with $$H^{-1}$$H-1 source terms

We establish the existence of liftings into discrete subspaces of \(\varvec{H}({{\mathrm{div}}})\) of piecewise polynomial data on locally refined simplicial partitions of polygonal/polyhedral domains. Our liftings are robust with respect to the polynomial degree. This result has important applications in the a posteriori error analysis of parabolic problems, where it permits the removal of so-called transition conditions that link two consecutive meshes. It can also be used in the a posteriori error analysis of elliptic problems, where it allows the treatment of meshes with arbitrary numbers of hanging nodes between elements. We present a constructive proof based on the a posteriori error analysis of an auxiliary elliptic problem with \(H^{-1}\) source terms, thereby yielding results of independent interest. In particular, for such problems, we obtain guaranteed upper bounds on the error along with polynomial-degree robust local efficiency of the estimators.     

Finite element simulation of a highly sensitive SH-SAW delay line sensor with SiO $$_{2}$$ 2 micro-ridges

Microsystem Technologies - The paper presents 3D finite element simulation of an SH-SAW delay line sensor to investigate coupled resonance with SiO $$_{2}$$ micro-ridges designed along the...     

A New Conjugate Gradient Method with Smoothing $$L_{1/2} $$ Regularization Based on a Modified Secant Equation for Training Neural Networks

Proposed in this paper is a new conjugate gradient method with smoothing \(L_{1/2} \) regularization based on a modified secant equation for training neural networks, where a descent search direction is generated by selecting an adaptive learning rate based on the strong Wolfe conditions. Two adaptive parameters are introduced such that the new training method possesses both quasi-Newton property and sufficient descent property. As shown in the numerical experiments for five benchmark classification problems from UCI repository, compared with the other conjugate gradient training algorithms, the new training algorithm has roughly the same or even better learning capacity, but significantly better generalization capacity and network sparsity. Under mild assumptions, a global convergence result of the proposed training method is also proved.