q-Deformation of the Krichever-Novikov Algebra

The recent focus on deformations of algebras called quantum algebras can be attributed to the fact that they appear to be the basic algebraic structures underlying an amazingly diverse set of physical situations. To date many interesting features of these algebras have been found and they are now known to belong to a class of algebras called Hopf algebras [1]. The remarkable aspect of these structures is that they can be regarded as deformations of the usual Lie algebras. Of late, there has been a considerable interest in the deformation of the Virasoro algebra and the underlying Heisenberg algebra [2-11]. In this letter we focus our attention on deforming generalizations of these algebras, namely the Krichever-Novikov (KN) algebra and its associated Heisenberg algebra.Comment: AmsTex. To appear in Letters in Mathematical Physic

Symmetric Multiplets in Quantum Algebras

We consider a modified version of the coproduct for \U(\su_q(2)) and show that in the limit when $q \rightarrow 1$, there exists an essentially non-cocommutative coproduct. We study the implications of this non-cocommutativity for a system of two spin-$1/2$ particles. Here it is shown that, unlike the usual case, this non-trivial coproduct allows for symmetric and anti-symmetric states to be present in the multiplet. We surmise that our analysis could be related to the ferromagnetic and antiferromagnetic cases of the Heisenberg magnets.Comment: Needs subeqnarray.sty. To be published in Mod Phys Lett.

Quantum cryptography based on qutrit Bell inequalities

We present a cryptographic protocol based upon entangled qutrit pairs. We analyze the scheme under a symmetric incoherent attack and plot the region for which the protocol is secure and compare this with the region of violations of certain Bell inequalities

Einstein Manifolds As Yang-Mills Instantons

It is well-known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equations from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang-Mills gauge theory and so Einstein manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)_L instantons and SU(2)_R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.Comment: v4; 17 pages, published version in Mod. Phys. Lett.

Entanglement of an impurity and conduction spins in the Kondo model

Based on Yosida's ground state of the single-impurity Kondo Hamiltonian, we study three kinds of entanglement between an impurity and conduction electron spins. First, it is shown that the impurity spin is maximally entangled with all the conduction electrons. Second, a two-spin density matrix of the impurity spin and one conduction electron spin is given by a Werner state. We find that the impurity spin is not entangled with one conduction electron spin even within the Kondo screening length $\xi_K$, although there is the spin-spin correlation between them. Third, we show the density matrix of two conduction electron spins is nearly same to that of a free electron gas. The single impurity does not change the entanglement structure of the conduction electrons in contrast to the dramatic change in electrical resistance.Comment: 5 pages, 2 figures, accepted for publication in Physical Review

Molecular beam epitaxial growth of high-quality InSb on InP and GaAs substrates

Epitaxial layers of InSb were grown on InP and GaAs substrates by molecular beam epitaxy. The dependence of the epilayer quality on flux ratio, J sub Sb4/J sub In, was studied. Deviation from an optimum value of J sub Sb4/J sub In (approx. 2) during growth led to deterioration in the surface morphology and the electrical and crystalline qualities of the films. Room temperature electron mobilities as high as 70,000 and 53,000 sq cm /V-s were measured in InSb layers grown on InP and GaAs substrates, respectively. Unlike the previous results, the conductivity in these films is n-type even at T = 13 K, and no degradation of the electron mobility due to the high density of dislocations was observed. The measured electron mobilities (and carrier concentrations) at 77 K in InSb layers grown on InP and GaAs substrates are 110,000 sq cm/V-s (3 x 10(15) cm(-3)) and 55,000 sq cm/V-s (4.95 x 10(15) cm(-3)), respectively, suggesting their application to electronic devices at cryogenic temperatures

Experimental Demonstration of Quantum State Multi-meter and One-qubit Fingerprinting in a Single Quantum Device

We experimentally demonstrate in NMR a quantum interferometric multi-meter for extracting certain properties of unknown quantum states without resource to quantum tomography. It can perform direct state determinations, eigenvalue/eigenvector estimations, purity tests of a quantum system, as well as the overlap of any two unknown quantum states. Using the same device, we also demonstrate one-qubit quantum fingerprinting