The Lie Algebraic Significance of Symmetric Informationally Complete Measurements

Examples of symmetric informationally complete positive operator valued measures (SIC-POVMs) have been constructed in every dimension less than or equal to 67. However, it remains an open question whether they exist in all finite dimensions. A SIC-POVM is usually thought of as a highly symmetric structure in quantum state space. However, its elements can equally well be regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the resulting structure constants, which are calculated from the traces of the triple products of the SIC-POVM elements and which, it turns out, characterize the SIC-POVM up to unitary equivalence. We show that the structure constants have numerous remarkable properties. In particular we show that the existence of a SIC-POVM in dimension d is equivalent to the existence of a certain structure in the adjoint representation of gl(d,C). We hope that transforming the problem in this way, from a question about quantum state space to a question about Lie algebras, may help to make the existence problem tractable.Comment: 56 page

Symmetric Informationally Complete Measurements of Arbitrary Rank

There has been much interest in so-called SIC-POVMs: rank 1 symmetric informationally complete positive operator valued measures. In this paper we discuss the larger class of POVMs which are symmetric and informationally complete but not necessarily rank 1. This class of POVMs is of some independent interest. In particular it includes a POVM which is closely related to the discrete Wigner function. However, it is interesting mainly because of the light it casts on the problem of constructing rank 1 symmetric informationally complete POVMs. In this connection we derive an extremal condition alternative to the one derived by Renes et al.Comment: Contribution to proceedings of International Conference on Quantum Optics, Minsk, 200

Bases for qudits from a nonstandard approach to SU(2)

Bases of finite-dimensional Hilbert spaces (in dimension d) of relevance for quantum information and quantum computation are constructed from angular momentum theory and su(2) Lie algebraic methods. We report on a formula for deriving in one step the (1+p)p qupits (i.e., qudits with d = p a prime integer) of a complete set of 1+p mutually unbiased bases in C^p. Repeated application of the formula can be used for generating mutually unbiased bases in C^d with d = p^e (e > or = 2) a power of a prime integer. A connection between mutually unbiased bases and the unitary group SU(d) is briefly discussed in the case d = p^e.Comment: From a talk presented at the 13th International Conference on Symmetry Methods in Physics (Dubna, Russia, 6-9 July 2009) organized in memory of Prof. Yurii Fedorovich Smirnov by the Bogoliubov Laboratory of Theoretical Physics of the JINR and the ICAS at Yerevan State University

Predictive use of the Maximum Entropy Production principle for Past and Present Climates

In this paper, we show how the MEP hypothesis may be used to build simple climate models without representing explicitly the energy transport by the atmosphere. The purpose is twofold. First, we assess the performance of the MEP hypothesis by comparing a simple model with minimal input data to a complex, state-of-the-art General Circulation Model. Next, we show how to improve the realism of MEP climate models by including climate feedbacks, focusing on the case of the water-vapour feedback. We also discuss the dependence of the entropy production rate and predicted surface temperature on the resolution of the model

Tight informationally complete quantum measurements

We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, "as close as possible" to orthonormal bases for the space of quantum states. These measures are distinguished by an exceptionally simple state-reconstruction formula which allows "painless" quantum state tomography. Complete sets of mutually unbiased bases and symmetric informationally complete positive-operator-valued measures are both members of this class, the latter being the unique minimal rank-one members. Recast as ensembles of pure quantum states, the rank-one members are in fact equivalent to weighted 2-designs in complex projective space. These measures are shown to be optimal for quantum cloning and linear quantum state tomography.Comment: 20 pages. Final versio

Variations on a theme of Heisenberg, Pauli and Weyl

The parentage between Weyl pairs, generalized Pauli group and unitary group is investigated in detail. We start from an abstract definition of the Heisenberg-Weyl group on the field R and then switch to the discrete Heisenberg-Weyl group or generalized Pauli group on a finite ring Z_d. The main characteristics of the latter group, an abstract group of order d**3 noted P_d, are given (conjugacy classes and irreducible representation classes or equivalently Lie algebra of dimension d**3 associated with P_d). Leaving the abstract sector, a set of Weyl pairs in dimension d is derived from a polar decomposition of SU(2) closely connected to angular momentum theory. Then, a realization of the generalized Pauli group P_d and the construction of generalized Pauli matrices in dimension d are revisited in terms of Weyl pairs. Finally, the Lie algebra of the unitary group U(d) is obtained as a subalgebra of the Lie algebra associated with P_d. This leads to a development of the Lie algebra of U(d) in a basis consisting of d**2 generalized Pauli matrices. In the case where d is a power of a prime integer, the Lie algebra of SU(d) can be decomposed into d-1 Cartan subalgebras.Comment: Dedicated to the memory of Mosh\'e Flato on the occasion of the tenth anniversary of his deat

Quantum channels and memory effects

Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information. Quantum information provides a theoretical framework and the proper mathematical tools to accomplish this. In this context the notion of codes and communication capacities have been introduced by generalizing them from the classical Shannon theory of information transmission and error correction. The underlying assumption of this approach is to consider the channel not as acting on a single system, but on sequences of systems, which, when properly initialized allow one to overcome the noisy effects induced by the physical process under consideration. While most of the work produced so far has been focused on the case in which a given channel transformation acts identically and independently on the various elements of the sequence (memoryless configuration in jargon), correlated error models appear to be a more realistic way to approach the problem. A slightly different, yet conceptually related, notion of correlated errors applies to a single quantum system which evolves continuously in time under the influence of an external disturbance which acts on it in a non-Markovian fashion. This leads to the study of memory effects in quantum channels: a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics. A survey is taken of the field of quantum channels theory while also embracing these specific and complex settings.Comment: Review article, 61 pages, 26 figures; 400 references. Final version of the manuscript, typos correcte

Salmonella Typhimurium Type III Secretion Effectors Stimulate Innate Immune Responses in Cultured Epithelial Cells

Recognition of conserved bacterial products by innate immune receptors leads to inflammatory responses that control pathogen spread but that can also result in pathology. Intestinal epithelial cells are exposed to bacterial products and therefore must prevent signaling through innate immune receptors to avoid pathology. However, enteric pathogens are able to stimulate intestinal inflammation. We show here that the enteric pathogen Salmonella Typhimurium can stimulate innate immune responses in cultured epithelial cells by mechanisms that do not involve receptors of the innate immune system. Instead, S. Typhimurium stimulates these responses by delivering through its type III secretion system the bacterial effector proteins SopE, SopE2, and SopB, which in a redundant fashion stimulate Rho-family GTPases leading to the activation of mitogen-activated protein (MAP) kinase and NF-κB signaling. These observations have implications for the understanding of the mechanisms by which Salmonella Typhimurium induces intestinal inflammation as well as other intestinal inflammatory pathologies

Prevention and Mitigation of Acute Radiation Syndrome in Mice by Synthetic Lipopeptide Agonists of Toll-Like Receptor 2 (TLR2)

Bacterial lipoproteins (BLP) induce innate immune responses in mammals by activating heterodimeric receptor complexes containing Toll-like receptor 2 (TLR2). TLR2 signaling results in nuclear factor-kappaB (NF-κB)-dependent upregulation of anti-apoptotic factors, anti-oxidants and cytokines, all of which have been implicated in radiation protection. Here we demonstrate that synthetic lipopeptides (sLP) that mimic the structure of naturally occurring mycoplasmal BLP significantly increase mouse survival following lethal total body irradiation (TBI) when administered between 48 hours before and 24 hours after irradiation. The TBI dose ranges against which sLP are effective indicate that sLP primarily impact the hematopoietic (HP) component of acute radiation syndrome. Indeed, sLP treatment accelerated recovery of bone marrow (BM) and spleen cellularity and ameliorated thrombocytopenia of irradiated mice. sLP did not improve survival of irradiated TLR2-knockout mice, confirming that sLP-mediated radioprotection requires TLR2. However, sLP was radioprotective in chimeric mice containing TLR2-null BM on a wild type background, indicating that radioprotection of the HP system by sLP is, at least in part, indirect and initiated in non-BM cells. sLP injection resulted in strong transient induction of multiple cytokines with known roles in hematopoiesis, including granulocyte colony-stimulating factor (G-CSF), keratinocyte chemoattractant (KC) and interleukin-6 (IL-6). sLP-induced cytokines, particularly G-CSF, are likely mediators of the radioprotective/mitigative activity of sLP. This study illustrates the strong potential of LP-based TLR2 agonists for anti-radiation prophylaxis and therapy in defense and medical scenarios