Short-wavelength secondary instabilities in homogeneous and stably stratified shear flows

We present a numerical investigation of three-dimensional, short-wavelength linear instabilities in Kelvin-Helmholtz (KH) vortices in homogeneous and stratified environments. The base flow, generated using two-dimensional numerical simulations, is characterized by the Reynolds number and the Richardson number defined based on the initial one-dimensional velocity and buoyancy profiles. The local stability equations are then solved on closed streamlines in the vortical base flow, which is assumed quasi-steady. For the unstratified case, the elliptic instability at the vortex core dominates at early times, before being taken over by the hyperbolic instability at the vortex edge. For the stratified case, the early time instabilities comprise a dominant elliptic instability at the core and a hyperbolic instability strongly influenced by stratification at the vortex edge. At intermediate times, the local approach shows a new branch of instability (convective branch) that emerges at the vortex core and subsequently moves towards the vortex edge. A few more convective instability branches appear at the vortex core and move away, before coalescing to form the most unstable region inside the vortex periphery at large times. The dominant instability characteristics from the local approach are shown to be in good qualitative agreement with results from global instability studies for both homogeneous and stratified cases. Compartmentalized analyses are then used to elucidate the role of shear and stratification on the identified instabilities. The role of buoyancy is shown to be critical after the primary KH instability saturates, with the dominant convective instability shown to occur in regions with the strongest statically unstable layering. We conclude by highlighting the potentially insightful role that the local approach may offer in understanding the secondary instabilities in other flows.Comment: Submitted to J. Fluid Mech., 20 pages, 10 figure

Detection prospects of light pseudoscalar Higgs boson at the LHC

The discovery potential of light pseudo scalar Higgs boson for the mass range 10-60 GeV is explored. In the context of the next-to-minimal supersymmetric standard(NMSSM) model, the branching fraction of light pseudo scalar Higgs boson decaying to a pair of photon can be quite large. A pair of light pseudo scalar Higgs boson produced indirectly through the standard model Higgs boson decay yields multiple photons in the final state and the corresponding production rate is restricted by ATLAS data. Discussing the impact of this constraint in the NMSSM, the detection prospects of light pseudoscalar Higgs boson in the channel consisting of at least three photons, a lepton and missing transverse energy are reported. It is observed that the possibilities of finding the pseudoscalar Higgs boson for the above mass range are promising for an integrated luminosity $\mathcal{L}=100 \text{fb}^{-1}$ with moderate significances, which can reach to more than 5$\sigma$ for higher luminosity options.Comment: 24 pages, 4 figures, updated reference

Entanglement Patterns in Mutually Unbiased Basis Sets for N Prime-state Particles

A few simply-stated rules govern the entanglement patterns that can occur in mutually unbiased basis sets (MUBs), and constrain the combinations of such patterns that can coexist (ie, the stoichiometry) in full complements of p^N+1 MUBs. We consider Hilbert spaces of prime power dimension (as realized by systems of N prime-state particles, or qupits), where full complements are known to exist, and we assume only that MUBs are eigenbases of generalized Pauli operators, without using a particular construction. The general rules include the following: 1) In any MUB, a particular qupit appears either in a pure state, or totally entangled, and 2) in any full MUB complement, each qupit is pure in p+1 bases (not necessarily the same ones), and totally entangled in the remaining p^N-p. It follows that the maximum number of product bases is p+1, and when this number is realized, all remaining p^N-p bases in the complement are characterized by the total entanglement of every qupit. This "standard distribution" is inescapable for two qupits (of any p), where only product and generalized Bell bases are admissible MUB types. This and the following results generalize previous results for qubits and qutrits. With three qupits there are three MUB types, and a number of combinations (p+2) are possible in full complements. With N=4, there are 6 MUB types for p=2, but new MUB types become possible with larger p, and these are essential to the realization of full complements. With this example, we argue that new MUB types, showing new entanglement characteristics, should enter with every step in N, and when N is a prime plus 1, also at critical p values, p=N-1. Such MUBs should play critical roles in filling complements.Comment: 27 pages, one figure, to be submitted to Physical Revie

Write Channel Model for Bit-Patterned Media Recording

We propose a new write channel model for bit-patterned media recording that reflects the data dependence of write synchronization errors. It is shown that this model accommodates both substitution-like errors and insertion-deletion errors whose statistics are determined by an underlying channel state process. We study information theoretic properties of the write channel model, including the capacity, symmetric information rate, Markov-1 rate and the zero-error capacity.Comment: 11 pages, 12 figures, journa

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

Mermin's Pentagram as an Ovoid of PG(3,2)

Mermin's pentagram, a specific set of ten three-qubit observables arranged in quadruples of pairwise commuting ones into five edges of a pentagram and used to provide a very simple proof of the Kochen-Specker theorem, is shown to be isomorphic to an ovoid (elliptic quadric) of the three-dimensional projective space of order two, PG(3,2). This demonstration employs properties of the real three-qubit Pauli group embodied in the geometry of the symplectic polar space W(5,2) and rests on the facts that: 1) the four observables/operators on any of the five edges of the pentagram can be viewed as points of an affine plane of order two, 2) all the ten observables lie on a hyperbolic quadric of the five-dimensional projective space of order two, PG(5,2), and 3) that the points of this quadric are in a well-known bijective correspondence with the lines of PG(3,2).Comment: 5 pages, 4 figure

Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres

A diagrammatic representation is given of the 24 rays of Peres that makes it easy to pick out all the 512 parity proofs of the Kochen-Specker theorem contained in them. The origin of this representation in the four-dimensional geometry of the rays is pointed out.Comment: 14 pages, 6 figures and 3 tables. Three references have been added. Minor typos have been correcte

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

Solution to the Mean King's problem with mutually unbiased bases for arbitrary levels

The Mean King's problem with mutually unbiased bases is reconsidered for arbitrary d-level systems. Hayashi, Horibe and Hashimoto [Phys. Rev. A 71, 052331 (2005)] related the problem to the existence of a maximal set of d-1 mutually orthogonal Latin squares, in their restricted setting that allows only measurements of projection-valued measures. However, we then cannot find a solution to the problem when e.g., d=6 or d=10. In contrast to their result, we show that the King's problem always has a solution for arbitrary levels if we also allow positive operator-valued measures. In constructing the solution, we use orthogonal arrays in combinatorial design theory.Comment: REVTeX4, 4 page