Entanglement enhanced classical capacity of quantum communication channels with correlated noise in arbitrary dimensions

We study the capacity of d-dimensional quantum channels with memory modeled by correlated noise. We show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher values of mutual information than product states. Moreover, a strong dependence of this effect on the nature of the noise correlations as well as on the parity of the space dimension is found. We conjecture that when entanglement gives an advantage in terms of mutual information, maximally entangled states saturate the channel capacity.Comment: 10 pages, 5 figure

Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs

We address the question of the multiplicativity of the maximal p-norm output purities of bosonic Gaussian channels under Gaussian inputs. We focus on general Gaussian channels resulting from the reduction of unitary dynamics in larger Hilbert spaces. It is shown that the maximal output purity of tensor products of single-mode channels under Gaussian inputs is multiplicative for any p>1 for products of arbitrary identical channels as well as for a large class of products of different channels. In the case of p=2 multiplicativity is shown to be true for arbitrary products of generic channels acting on any number of modes.Comment: 9 page

Relativistic Doppler effect in quantum communication

When an electromagnetic signal propagates in vacuo, a polarization detector cannot be rigorously perpendicular to the wave vector because of diffraction effects. The vacuum behaves as a noisy channel, even if the detectors are perfect. The ``noise'' can however be reduced and nearly cancelled by a relative motion of the observer toward the source. The standard definition of a reduced density matrix fails for photon polarization, because the transversality condition behaves like a superselection rule. We can however define an effective reduced density matrix which corresponds to a restricted class of positive operator-valued measures. There are no pure photon qubits, and no exactly orthogonal qubit states.Comment: 10 pages LaTe

Minimum output entropy of bosonic channels: a conjecture

The von Neumann entropy at the output of a bosonic channel with thermal noise is analyzed. Coherent-state inputs are conjectured to minimize this output entropy. Physical and mathematical evidence in support of the conjecture is provided. A stronger conjecture--that output states resulting from coherent-state inputs majorize the output states from other inputs--is also discussed.Comment: 15 pages, 12 figure

Notes on multiplicativity of maximal output purity for completely positive qubit maps

A problem in quantum information theory that has received considerable attention in recent years is the question of multiplicativity of the so-called maximal output purity (MOP) of a quantum channel. This quantity is defined as the maximum value of the purity one can get at the output of a channel by varying over all physical input states, when purity is measured by the Schatten $q$-norm, and is denoted by $\nu_q$. The multiplicativity problem is the question whether two channels used in parallel have a combined $\nu_q$ that is the product of the $\nu_q$ of the two channels. A positive answer would imply a number of other additivity results in QIT. Very recently, P. Hayden has found counterexamples for every value of $q>1$. Nevertheless, these counterexamples require that the dimension of these channels increases with $1-q$ and therefore do not rule out multiplicativity for $q$ in intervals $[1,q_0)$ with $q_0$ depending on the channel dimension. I argue that this would be enough to prove additivity of entanglement of formation and of the classical capacity of quantum channels. More importantly, no counterexamples have as yet been found in the important special case where one of the channels is a qubit-channel, i.e. its input states are 2-dimensional. In this paper I focus attention to this qubit case and I rephrase the multiplicativity conjecture in the language of block matrices and prove the conjecture in a number of special cases.Comment: Manuscript for a talk presented at the SSPCM07 conference in Myczkowce, Poland, 10/09/2007. 12 page

Nonadditivity effects in classical capacities of quantum multiple-access channels

We study classical capacities of quantum multi-access channels in geometric terms revealing breaking of additivity of Holevo-like capacity. This effect is purely quantum since, as one points out, any classical multi-access channels have their regions additive. The observed non-additivity in quantum version presented here seems to be the first effect of this type with no additional resources like side classical or quantum information (or entanglement) involved. The simplicity of quantum channels involved resembles butterfly effect in case of classical channel with two senders and two receivers.Comment: 5 pages, 5 figure

Self-Propagating High-Temperature Synthesis of Silicon Carbide and Silicon Nitride Nanopowders Composition using Sodium Azide and Halides

Regularities of self-propagating high-temperature synthesis (SHS) or combustion synthesis (CS) by using “silicon – sodium azide – ammonium hexafluorosilicate – carbon – aluminum” powder mixture in the nitrogen atmosphere were investigated. The thermodynamic analysis of the combustion synthesis was performed. Experimental investigation of the combustion process: the measurement of linear rates of the combustion front propagation and the maximum combustion temperatures was conducted in a laboratory reactor with working volume 4.5 liters. The influence of the components ratio in the initial mixture on the combustion temperature, combustion rate and composition of reaction product was studied. The phase composition of the product synthesized was determined with an X-ray diffractometer. It was disclosed that the SHS product consists of the composition (mixture) of silicon carbide nanopowder with silicon nitride whiskers and a final halide. Investigation of surface topography and morphology of the product particles was carried out with a scanning electron microscope. Optimal mixture for the synthesis of nanoscale composition based on silicon carbide was determined: “14Si+6NaN3+(NH4)2SiF6+15C+Al”. In this case, the SHS product consists of four phases: silicon carbide (β-SiC) – 48.57 wt.%, α-silicon nitride (α-Si3N4) – 27.04 wt.%, β-silicon nitride (β-Si3N4) – 5.83 wt.%, and sodium hexafluoroaluminate (Na3AlF6) – 18.56 wt.%. The average particle size of the composition was in the range of 70–130 nm. It was shown that the composition of the silicon carbide with silicon nitride and the final halide Na3AlF6 playing a role a flux can be used as a modifier of castable aluminum alloys and as a reinforcing phase of aluminomatrix composites

Strictly contractive quantum channels and physically realizable quantum computers

We study the robustness of quantum computers under the influence of errors modelled by strictly contractive channels. A channel $T$ is defined to be strictly contractive if, for any pair of density operators $\rho,\sigma$ in its domain, $\| T\rho - T\sigma \|_1 \le k \| \rho-\sigma \|_1$ for some $0 \le k < 1$ (here $\| \cdot \|_1$ denotes the trace norm). In other words, strictly contractive channels render the states of the computer less distinguishable in the sense of quantum detection theory. Starting from the premise that all experimental procedures can be carried out with finite precision, we argue that there exists a physically meaningful connection between strictly contractive channels and errors in physically realizable quantum computers. We show that, in the absence of error correction, sensitivity of quantum memories and computers to strictly contractive errors grows exponentially with storage time and computation time respectively, and depends only on the constant $k$ and the measurement precision. We prove that strict contractivity rules out the possibility of perfect error correction, and give an argument that approximate error correction, which covers previous work on fault-tolerant quantum computation as a special case, is possible.Comment: 14 pages; revtex, amsfonts, amssymb; made some changes (recommended by Phys. Rev. A), updated the reference

Pauli Diagonal Channels Constant on Axes

We define and study the properties of channels which are analogous to unital qubit channels in several ways. A full treatment can be given only when the dimension d is a prime power, in which case each of the (d+1) mutually unbiased bases (MUB) defines an axis. Along each axis the channel looks like a depolarizing channel, but the degree of depolarization depends on the axis. When d is not a prime power, some of our results still hold, particularly in the case of channels with one symmetry axis. We describe the convex structure of this class of channels and the subclass of entanglement breaking channels. We find new bound entangled states for d = 3. For these channels, we show that the multiplicativity conjecture for maximal output p-norm holds for p=2. We also find channels with behavior not exhibited by unital qubit channels, including two pairs of orthogonal bases with equal output entropy in the absence of symmetry. This provides new numerical evidence for the additivity of minimal output entropy

Жидкофазное получение методом СВС и термическая обработка композитов на основе алюминиево-магниевых сплавов, упрочненных высокодисперсной фазой карбида титана

Aluminum matrix composites reinforced with ultra-fine refractory titanium carbide feature a unique combination of properties. They are promising structural materials. Self-propagating high-temperature synthesis (SHS) is an affordable and energy-saving composite making process. It involves the exothermic reaction between titanium and carbon (or their compounds) directly in the melt. We studied the properties of SHS composites based on the AMg2 and AMg6 commercially available alloys reinforced with 10 wt.%TiC. We investigated the macroand microstructure of the samples with XRD and EDS analysis. It was found that the β-phase is separated from α-solid solution of aluminum as early as the air cooling stage. We conducted experiments aimed at studying the effects of additional heating on the sample structure and properties and found the optimal temperature and time values. We also proposed a phenomenological model of the structural transformation sequence. We compared the physical, mechanical, and manufacturing properties and corrosion resistance of the original cold-hardened AMg2N and AMg6N alloys and the composites before and after heat treatment. It was found that additional heating reduces porosity and maintains electrical conductivity. It was also found that the compressive strength and relative strain of the composite based on the AMg2 alloy change insignificantly, while for the AMg6-based composite the reduction is more significant. Heat treatment increases the composite hardness while maintaining sufficient plastic deformation. It is confirmed by the measured values of the relative strain and the reduction ratio close to that of the original matrix alloys. It was also found that the composites retain high resistance to carbon dioxide and hydrogen sulfide corrosion.Алюмоматричные композиционные материалы, дисперсно-упрочненные тугоплавкой фазой карбида титана, характеризуются уникальным сочетанием свойств и относятся к группе перспективных конструкционных материалов. Одним из наиболее доступных и энергосберегающих методов их получения является самораспространяющийся высокотемпературный синтез (СВС), основанный  на  экзотермическом  взаимодействии  титана  и  углерода  (или  их  соединений)  непосредственно  в  расплаве. В работе приводятся результаты СВС композиционных материалов на основе промышленных сплавов АМг2H и АМг6H, упрочненных  10  мас.%TiC.  Исследованы  макро и  микроструктура  полученных  образцов,  проведены  микрорентгеноспектральный и рентгенофазовый анализы. Установлено, что уже в процессе охлаждения  на  воздухе  после  синтеза  происходит  выделение β-фазы из α-твердого раствора алюминия. Проведены эксперименты по изучению влияния дополнительного нагрева на структуру и свойства образцов, определены  оптимальные  температурно-временные  параметры,  предложена  феноменологическая модель последовательности структурных превращений. Выполнен сравнительный анализ физических, механических, технологических свойств и коррозионной стойкости исходных сплавов АМг2H и АМг6H в  нагартованном  состоянии  и  композиционных материалов на их основе до и после термической обработки. Установлено, что проведение дополнительного нагрева способствует снижению пористости и сохранению уровня электропроводности относительно этих показателей для литых композитов. Выявлено, что  прочность  на  сжатие  и  относительная  деформация  для  композита  на  основе  сплава  АМг2  изменяются незначительно, тогда как для материала на основе АМг6 их падение более существенно. При этом термическая обработка позволяет повысить твердость материалов, сохранив достаточную способность композитов к пластической деформации, что подтверждается значениями степени деформации и коэффициента уковки, близкими к уровню матричных сплавов. Также установлено,  что  синтезированные  композиционные  материалы  сохраняют  высокий  уровень  устойчивости  к  углекислотной и сероводородной коррозии