Prasanta K. Panigrahi

Quantum-information splitting using multipartite cluster states

We provide various schemes for the splitting up of quantum information into parts using four- and five-partite cluster states. Explicit protocols for the quantum information splitting (QIS) of single- and two-qubit states are illustrated. It is found that the four-partite cluster state can be used for QIS of an entangled state and the five-partite cluster state can be used for QIS of an arbitrary two-qubit state. The schemes considered here are also secure against certain eavesdropping attacks.

Quantum teleportation and state sharing using a genuinely entangled six-qubit state

The usefulness of the genuinely entangled six-qubit state that has recently been introduced by Borras et al (2007 J. Phys. A: Math. Theor. 40 13407) is investigated for the quantum teleportation of an arbitrary three-qubit state and for quantum state sharing (QSTS) of an arbitrary two-qubit state. We construct two distinct protocols for QSTS of an arbitrary two-qubit state using this state as an entangled channel. We construct 16 orthogonal four-qubit states which can lock an arbitrary two-qubit state between two parties.

BOUND STATE WAVE FUNCTIONS THROUGH THE QUANTUM HAMILTON–JACOBI FORMALISM

The bound state wave functions for a wide class of exactly solvable potentials are found by utilizing the quantum Hamilton–Jacobi formalism of Leacock and Padgett. It is shown that, exploiting the singularity structure of the quantum momentum function, until now used only for obtaining the bound state energies, one can straightforwardly find both the eigenvalues and the corresponding eigenfunctions. After demonstrating the working of this approach through a few solvable examples, we consider Hamiltonians, which exhibit broken and unbroken phases of supersymmetry. The natural emergence of the eigenspectra and the wave functions, in both unbroken and the algebraically nontrivial broken phase, demonstrates the utility of this formalism.

Complex solitons in Bose–Einstein condensates with two- and three-body interactions

For the first time, we find the complex solitons for a quasi-one-dimensional Bose-Einstein condensate with two-and three-body interactions. These localized solutions are characterized by a power law behaviour. Both dark and right solitons can be excited in the experimentally allowed parameter domain, when two-and three-body interactions are,respectively, repulsive and attractive. The dark solitons travel with a constant speed, which is quite different from the Lieb mode, where profiles with different speeds, bounded above by sound velocity, can exist for specified interaction strengths. We also study the properties of these solitons in the presence of harmonic confinement with time-dependent nonlinearity and loss. The modulational instability and the Vakhitov-Kolokolov criterion of stability are also studied.

Teleportation in the presence of common bath decoherence at the transmitting station

We investigate the effect of common bath decoherence on the qubits of Alice in the usual teleportation protocol. The system bath interaction is studied under the central spin model, where the qubits are coupled to the bath spins through isotropic Heisenberg interaction. We have given a more generalized representation of the protocol in terms of density matrices and calculated the average fidelity of the teleported state for different Bell state measurements performed by Alice. The common bath interaction differentiates the outcome of various Bell state measurements made by Alice. There will be a high fidelity teleportation for a singlet measurement made by Alice when both the qubits of Alice interact either ferromagnetically or antiferromagnetically with bath. In contrast if one of Alices qubits interacts ferromagnetically and the other antiferromagnetically then measurement of Bell states belonging to the triplet sector will give better fidelity. We have also evaluated the average fidelity when Alice prefers nonmaximally entangled states as her basis for measurement.

Detecting cervical cancer progression through extracted intrinsic fluorescence and principal component analysis

Abstract. Intrinsic fluorescence spectra of the human normal, cervical intraepithelial neoplasia 1 (CIN1), CIN2, and cervical cancer tissue have been extracted by effectively combining the measured polarized fluorescence and polarized elastic scattering spectra. The efficacy of principal component analysis (PCA) to disentangle the collective behavior from smaller correlated clusters in a dimensionally reduced space in conjunction with the intrinsic fluorescence is examined. This combination unambiguously reveals the biochemical changes occurring with the progression of the disease. The differing activities of the dominant fluorophores, collagen, nicotinamide adenine dinucleotide, flavins, and porphyrin of different grades of precancers are clearly identified through a careful examination of the sectorial behavior of the dominant eigenvectors of PCA. To further classify the different grades, the Mahalanobis distance has been calculated using the scores of selected principal components.

Exceptional orthogonal polynomials, QHJ formalism and SWKB quantization condition

We study the quantum Hamilton–Jacobi (QHJ) equation of the recently obtained exactly solvable models, related to the newly discovered exceptional polynomials, and show that the QHJ formalism reproduces the exact eigenvalues and the eigenfunctions. The fact that the eigenfunctions have zeros and poles in complex locations leads to an unconventional singularity structure of the quantum momentum function p(x), the logarithmic derivative of the wavefunction, which forms the crux of the QHJ approach to quantization. A comparison of the singularity structure for these systems with the known exactly solvable and quasi-exactly solvable models reveals interesting differences. We find that the singularity structure of the momentum function for these new potentials lies between the above two distinct models, sharing similarities with both of them. This prompted us to examine the exactness of the supersymmetric Wentzel–Kramers–Brillouin (SWKB) quantization condition. The interesting singularity structure of p(x) and of the superpotential for these models has important consequences for the SWKB rule and in our proof of its exactness for these quantal systems.

Non-destructive discrimination of Bell states by NMR using a single ancilla qubit

Discrimination of Bell states plays an important role in a number of quantum computational protocols such as teleportation and secret sharing. However, most of the protocols dealing with Bell state discrimination in the literature either involve performing correlated measurements or destroying the entanglement of the system. Here, we demonstrate an NMR-based experimental realization of a protocol for Bell state discrimination, following a scheme proposed by Gupta et al (quant-ph/0504183v1, 23 April 2005), which does not destroy the Bell state under consideration. Using the proposed protocol, one can deterministically distinguish the Bell states, without performing a measurement using the entangled basis. State discrimination is performed through two independent measurements on one ancilla qubit, which leaves the Bell states unchanged.

Diagnosing Heterogeneous Dynamics for CT Scan Images of Human Brain in Wavelet and MFDFA Domain

CT scan images of human brain of a particular patient in different cross sections are taken, on which wavelet transform and multi-fractal analysis are applied. The vertical and horizontal unfolding of images are done before analyzing these images. A systematic investigation of de-noised CT scan images of human brain in different cross-sections are carried out through wavelet normalized energy and wavelet semi-log plots, which clearly points out the mismatch between results of vertical and horizontal unfolding. The mismatch of results confirms the heterogeneity in spatial domain. Using the multi-fractal de-trended fluctuation analysis (MFDFA), the mismatch between the values of Hurst exponent and width of singularity spectrum by vertical and horizontal unfolding confirms the same.

Loss of superfluidity in the Bose?Einstein condensate in an optical lattice with cubic and quintic nonlinearity

In a one-dimensional shallow optical lattice, in the presence of both cubic and quintic nonlinearity, a superfluid density wave is identified in a Bose?Einstein condensate. Interestingly, it ceases to exist when only one of these interactions is operative. We predict the loss of superfluidity through a classical dynamical phase transition, where modulational instability leads to the loss of phase coherence. In a certain parameter domain, the competition between lattice potential and the interactions is shown to give rise to a stripe phase, where atoms are confined in finite domains. In a pure two-body case, apart from the known superfluid and insulating phases, a density wave insulating phase is found to exist, possessing two frequency modulations commensurate with the lattice potential.