Quantum Kaleidoscopes and Bell's theorem

A quantum kaleidoscope is defined as a set of observables, or states, consisting of many different subsets that provide closely related proofs of the Bell-Kochen-Specker (BKS) and Bell nonlocality theorems. The kaleidoscopes prove the BKS theorem through a simple parity argument, which also doubles as a proof of Bell's nonlocality theorem if use is made of the right sort of entanglement. Three closely related kaleidoscopes are introduced and discussed in this paper: a 15-observable kaleidoscope, a 24-state kaleidoscope and a 60-state kaleidoscope. The close relationship of these kaleidoscopes to a configuration of 12 points and 16 lines known as Reye's configuration is pointed out. The "rotations" needed to make each kaleidoscope yield all its apparitions are laid out. The 60-state kaleidoscope, whose underlying geometrical structure is that of ten interlinked Reye's configurations (together with their duals), possesses a total of 1120 apparitions that provide proofs of the two Bell theorems. Some applications of these kaleidoscopes to problems in quantum tomography and quantum state estimation are discussed.Comment: Two new references (No. 21 and 22) to related work have been adde

Characterization of Binary Constraint System Games

We consider a class of nonlocal games that are related to binary constraint systems (BCSs) in a manner similar to the games implicit in the work of Mermin [N.D. Mermin, "Simple unified form for the major no-hidden-variables theorems," Phys. Rev. Lett., 65(27):3373-3376, 1990], but generalized to n binary variables and m constraints. We show that, whenever there is a perfect entangled protocol for such a game, there exists a set of binary observables with commutations and products similar to those exhibited by Mermin. We also show how to derive upper bounds strictly below 1 for the the maximum entangled success probability of some BCS games. These results are partial progress towards a larger project to determine the computational complexity of deciding whether a given instance of a BCS game admits a perfect entangled strategy or not.Comment: Revised version corrects an error in the previous version of the proof of Theorem 1 that arises in the case of POVM measurement

Structure and sequence analyses of Bacteroides proteins BVU_4064 and BF1687 reveal presence of two novel predominantly-beta domains, predicted to be involved in lipid and cell surface interactions.

BackgroundN-terminal domains of BVU_4064 and BF1687 proteins from Bacteroides vulgatus and Bacteroides fragilis respectively are members of the Pfam family PF12985 (DUF3869). Proteins containing a domain from this family can be found in most Bacteroides species and, in large numbers, in all human gut microbiome samples. Both BVU_4064 and BF1687 proteins have a consensus lipobox motif implying they are anchored to the membrane, but their functions are otherwise unknown. The C-terminal half of BVU_4064 is assigned to protein family PF12986 (DUF3870); the equivalent part of BF1687 was unclassified.ResultsCrystal structures of both BVU_4064 and BF1687 proteins, solved at the JCSG center, show strikingly similar three-dimensional structures. The main difference between the two is that the two domains in the BVU_4064 protein are connected by a short linker, as opposed to a longer insertion made of 4 helices placed linearly along with a strand that is added to the C-terminal domain in the BF1687 protein. The N-terminal domain in both proteins, corresponding to the PF12985 (DUF3869) domain is a β-sandwich with pre-albumin-like fold, found in many proteins belonging to the Transthyretin clan of Pfam. The structures of C-terminal domains of both proteins, corresponding to the PF12986 (DUF3870) domain in BVU_4064 protein and an unclassified domain in the BF1687 protein, show significant structural similarity to bacterial pore-forming toxins. A helix in this domain is in an analogous position to a loop connecting the second and third strands in the toxin structures, where this loop is implicated to play a role in the toxin insertion into the host cell membrane. The same helix also points to the groove between the N- and C-terminal domains that are loosely held together by hydrophobic and hydrogen bond interactions. The presence of several conserved residues in this region together with these structural determinants could make it a functionally important region in these proteins.ConclusionsStructural analysis of BVU_4064 and BF1687 points to possible roles in mediating multiple interactions on the cell-surface/extracellular matrix. In particular the N-terminal domain could be involved in adhesive interactions, the C-terminal domain and the inter-domain groove in lipid or carbohydrate interactions

Quantum entanglement: The unitary 8-vertex braid matrix with imaginary rapidity

We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the "canonical factorization" of the coefficients of the projectors spanning the basis. This adds one more new facet to the famous and fascinating features of the 8-vertex model. The double periodicity and the analytic properties of the elliptic functions involved lead to a rich structure of the 3-tangle quantifying the entanglement. We thus explore the complex relationship between topological and quantum entanglement.Comment: 4 pages in REVTeX format, 2 figure

On the structure of the sets of mutually unbiased bases for N qubits

For a system of N qubits, spanning a Hilbert space of dimension d=2^N, it is known that there exists d+1 mutually unbiased bases. Different construction algorithms exist, and it is remarkable that different methods lead to sets of bases with different properties as far as separability is concerned. Here we derive the four sets of nine bases for three qubits, and show how they are unitarily related. We also briefly discuss the four-qubit case, give the entanglement structure of sixteen sets of bases,and show some of them, and their interrelations, as examples. The extension of the method to the general case of N qubits is outlined.Comment: 16 pages, 10 tables, 1 figur

Genomic donor cassette sharing during VLRA and VLRC assembly in jawless vertebrates

Lampreys possess two T-like lymphocyte lineages that express either variable lymphocyte receptor (VLR) A or VLRC antigen receptors. VLRA+ and VLRC+ lymphocytes share many similarities with the two principal T-cell lineages of jawed vertebrates expressing the αβ and γδ T-cell receptors (TCRs). During the assembly of VLR genes, several types of genomic cassettes are inserted, in step-wise fashion, into incomplete germ-line genes to generate the mature forms of antigen receptor genes. Unexpectedly, the structurally variable components of VLRA and VLRC receptors often possess partially identical sequences; this phenomenon of module sharing between these two VLR isotypes occurs in both lampreys and hagfishes. By contrast, VLRA and VLRC molecules typically do not share their building blocks with the structurally analogous VLRB receptors that are expressed by B-like lymphocytes. Our studies reveal that VLRA and VLRC germ-line genes are situated in close proximity to each other in the lamprey genome and indicate the interspersed arrangement of isotype-specific and shared genomic donor cassettes; these features may facilitate the shared cassette use. The genomic structure of the VLRA/VLRC locus in lampreys is reminiscent of the interspersed nature of the TCRA/TCRD locus in jawed vertebrates that also allows the sharing of some variable gene segments during the recombinatorial assembly of TCR genes

AAA+: A class of chaperone-like ATPases associated with the assembly, operation, and disassembly of protein complexes

Using a combination of computer methods for iterative database searches and multiple sequence alignment, we show that protein sequences related to the AAA family of ATPases are far more prevalent than reported previously. Among these are regulatory components of Lon and Clp proteases, proteins involved in DNA replication, recombination, and restriction (including subunits of the origin recognition complex, replication factor C proteins, MCM DNA-licensing factors and the bacterial DnaA, RuvB, and McrB proteins), prokaryotic NtrC-related transcription regulators, the Bacillus sporulation protein SpoVJ, Mg2+, and Co2+ chelatases, the Halobacterium GvpN gas vesicle synthesis protein, dynein motor proteins, TorsinA, and Rubisco activase. Alignment of these sequences, in light of the structures of the clamp loader delta' subunit of Escherichia coli DNA polymerase III and the hexamerization component of N-ethylmaleimide-sensitive fusion protein, provides structural and mechanistic insights into these proteins, collectively designated the AAA+ class. Whole-genome analysis indicates that this class is ancient and has undergone considerable functional divergence prior to the emergence of the major divisions of life. These proteins often perform chaperone-like functions that assist in the assembly, operation, or disassembly of protein complexes. The hexameric architecture often associated with this class can provide a hole through which DNA or RNA can be thread; this may be important for assembly or remodeling of DNA-protein complexes

OST-HTH: a novel predicted RNA-binding domain

BACKGROUND: The mechanism by which the arthropod Oskar and vertebrate TDRD5/TDRD7 proteins nucleate or organize structurally related ribonucleoprotein (RNP) complexes, the polar granule and nuage, is poorly understood. Using sequence profile searches we identify a novel domain in these proteins that is widely conserved across eukaryotes and bacteria. RESULTS: Using contextual information from domain architectures, sequence-structure superpositions and available functional information we predict that this domain is likely to adopt the winged helix-turn-helix fold and bind RNA with a potential specificity for dsRNA. We show that in eukaryotes this domain is often combined in the same polypeptide with protein-protein- or lipid- interaction domains that might play a role in anchoring these proteins to specific cytoskeletal structures. CONCLUSIONS: Thus, proteins with this domain might have a key role in the recognition and localization of dsRNA, including miRNAs, rasiRNAs and piRNAs hybridized to their targets. In other cases, this domain is fused to ubiquitin-binding, E3 ligase and ubiquitin-like domains indicating a previously under-appreciated role for ubiquitination in regulating the assembly and stability of nuage-like RNP complexes. Both bacteria and eukaryotes encode a conserved family of proteins that combines this predicted RNA-binding domain with a previously uncharacterized domain (DUF88). We present evidence that it is an RNAse belonging to the superfamily that includes the 5'->3' nucleases, PIN and NYN domains and might be recruited to degrade certain RNAs. REVIEWERS: This article was reviewed by Sandor Pongor and Arcady Mushegian