Second quantized automorphisms of the renormalized square of white noise (RSWN) algebra

We determine the structure of the -endomorphisms of the RSWN algebra, induced by linear maps in the 1-particle Hilbert algebra, introduce the RSWN analogue of the free evolutions and nd the explicit form of the KMS states associated with some of them

Entangled inputs cannot make imperfect quantum channels perfect

Entangled inputs can enhance the capacity of quantum channels, this being one of the consequences of the celebrated result showing the non-additivity of several quantities relevant for quantum information science. In this work, we answer the converse question (whether entangled inputs can ever render noisy quantum channels have maximum capacity) to the negative: No sophisticated entangled input of any quantum channel can ever enhance the capacity to the maximum possible value; a result that holds true for all channels both for the classical as well as the quantum capacity. This result can hence be seen as a bound as to how "non-additive quantum information can be". As a main result, we find first practical and remarkably simple computable single-shot bounds to capacities, related to entanglement measures. As examples, we discuss the qubit amplitude damping and identify the first meaningful bound for its classical capacity.Comment: 5 pages, 2 figures, an error in the argument on the quantum capacity corrected, version to be published in the Physical Review Letter

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

On Hastings' counterexamples to the minimum output entropy additivity conjecture

Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. Furthermore, we prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension. This makes Hastings' original reasoning clearer and extends the class of channels for which additivity can be shown to be violated.Comment: 17 pages + 1 lin

Complete hierarchies of efficient approximations to problems in entanglement theory

We investigate several problems in entanglement theory from the perspective of convex optimization. This list of problems comprises (A) the decision whether a state is multi-party entangled, (B) the minimization of expectation values of entanglement witnesses with respect to pure product states, (C) the closely related evaluation of the geometric measure of entanglement to quantify pure multi-party entanglement, (D) the test whether states are multi-party entangled on the basis of witnesses based on second moments and on the basis of linear entropic criteria, and (E) the evaluation of instances of maximal output purities of quantum channels. We show that these problems can be formulated as certain optimization problems: as polynomially constrained problems employing polynomials of degree three or less. We then apply very recently established known methods from the theory of semi-definite relaxations to the formulated optimization problems. By this construction we arrive at a hierarchy of efficiently solvable approximations to the solution, approximating the exact solution as closely as desired, in a way that is asymptotically complete. For example, this results in a hierarchy of novel, efficiently decidable sufficient criteria for multi-particle entanglement, such that every entangled state will necessarily be detected in some step of the hierarchy. Finally, we present numerical examples to demonstrate the practical accessibility of this approach.Comment: 14 pages, 3 figures, tiny modifications, version to be published in Physical Review

The power of symmetric extensions for entanglement detection

In this paper, we present new progress on the study of the symmetric extension criterion for separability. First, we show that a perturbation of order O(1/N) is sufficient and, in general, necessary to destroy the entanglement of any state admitting an N Bose symmetric extension. On the other hand, the minimum amount of local noise necessary to induce separability on states arising from N Bose symmetric extensions with Positive Partial Transpose (PPT) decreases at least as fast as O(1/N^2). From these results, we derive upper bounds on the time and space complexity of the weak membership problem of separability when attacked via algorithms that search for PPT symmetric extensions. Finally, we show how to estimate the error we incur when we approximate the set of separable states by the set of (PPT) N -extendable quantum states in order to compute the maximum average fidelity in pure state estimation problems, the maximal output purity of quantum channels, and the geometric measure of entanglement.Comment: see Video Abstract at http://www.quantiki.org/video_abstracts/0906273

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

Newly identified climatically and environmentally significant high-latitude dust sources

Dust particles from high latitudes have a potentially large local, regional, and global significance to climate and the environment as short-lived climate forcers, air pollutants, and nutrient sources. Identifying the locations of local dust sources and their emission, transport, and deposition processes is important for understanding the multiple impacts of high-latitude dust (HLD) on the Earth's systems. Here, we identify, describe, and quantify the source intensity (SI) values, which show the potential of soil surfaces for dust emission scaled to values 0 to 1 concerning globally best productive sources, using the Global Sand and Dust Storms Source Base Map (G-SDS-SBM). This includes 64 HLD sources in our collection for the northern (Alaska, Canada, Denmark, Greenland, Iceland, Svalbard, Sweden, and Russia) and southern (Antarctica and Patagonia) high latitudes. Activity from most of these HLD sources shows seasonal character. It is estimated that high-latitude land areas with higher (SI ≥0.5), very high (SI ≥0.7), and the highest potential (SI ≥0.9) for dust emission cover >1 670 000 km2, >560 000 km2, and >240 000 km2, respectively. In the Arctic HLD region (≥60∘ N), land area with SI ≥0.5 is 5.5 % (1 035 059 km2), area with SI ≥0.7 is 2.3 % (440 804 km2), and area with SI ≥0.9 is 1.1 % (208 701 km2). Minimum SI values in the northern HLD region are about 3 orders of magnitude smaller, indicating that the dust sources of this region greatly depend on weather conditions. Our spatial dust source distribution analysis modeling results showed evidence supporting a northern HLD belt, defined as the area north of 50∘ N, with a “transitional HLD-source area” extending at latitudes 50–58∘ N in Eurasia and 50–55∘ N in Canada and a “cold HLD-source area” including areas north of 60∘ N in Eurasia and north of 58∘ N in Canada, with currently “no dust source” area between the HLD and low-latitude dust (LLD) dust belt, except for British Columbia. Using the global atmospheric transport model SILAM, we estimated that 1.0 % of the global dust emission originated from the high-latitude regions. About 57 % of the dust deposition in snow- and ice-covered Arctic regions was from HLD sources. In the southern HLD region, soil surface conditions are favorable for dust emission during the whole year. Climate change can cause a decrease in the duration of snow cover, retreat of glaciers, and an increase in drought, heatwave intensity, and frequency, leading to the increasing frequency of topsoil conditions favorable for dust emission, which increases the probability of dust storms. Our study provides a step forward to improve the representation of HLD in models and to monitor, quantify, and assess the environmental and climate significance of HLD

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