Anu Venugopalan

An Integrated Hierarchical Dynamic Quantum Secret Sharing Protocol

Generalizing the notion of dynamic quantum secret sharing (DQSS), a simplified protocol for hierarchical dynamic quantum secret sharing (HDQSS) is proposed and it is shown that the protocol can be implemented using any existing protocol of quantum key distribution, quantum key agreement or secure direct quantum communication. The security of this proposed protocol against eavesdropping and collusion attacks is discussed with specific attention towards the issues related to the composability of the subprotocols that constitute the proposed protocol. The security and qubit efficiency of the proposed protocol is also compared with that of other existing protocols of DQSS. Further, it is shown that it is possible to design a semi-quantum protocol of HDQSS and in principle, the protocols of HDQSS can be implemented using any quantum state. It is also noted that the completely orthogonal-state-based realization of HDQSS protocol is possible and that HDQSS can be experimentally realized using a large number of alternative approaches.

Environment-induced decoherence I. The Stern-Gerlach measurement

A dynamical model for the collapse of the wave function in a quantum measurement process is proposed by considering the interaction of a quantum system (spin -12) with a macroscopic quantum apparatus interacting with an environment in a dissipative manner. The dissipative interaction leads to decoherence in the superposition states of the apparatus, making its behaviour classical in the sense that the density matrix becomes diagonal with time. Since the apparatus is also interacting with the system, the probabilities of the diagonal density matrix are determined by the state vector of the system. We consider a Stern-Gerlach type model, where a spin-12 particle is in an inhomogeneous magnetic field, the whole set up being in contact with a large environment. Here we find that the density matrix of the combined system and apparatus becomes diagonal and the momentum of the particle becomes correlated with a spin operator, selected by the choice of the system-apparatus interaction. This allows for a measurement of spin via a momentum measurement on the particle with associated probabilities in accordance with quantum principles.

DECOHERENCE AND MATTER WAVE INTERFEROMETRY

A two-slit interference of a massive particle in the presence of environment-induced decoherence is theoretically analyzed. The Markovian Master equation, derived from coupling the particle to a harmonic-oscillator heat bath, is used to obtain exact solutions which show the existence of an interference pattern. Interestingly, decoherence does not affect the pattern, but only leads to a reduction in the fringe visibility.

Energy basis via decoherence

The question of the emergence of a preferred basis which is generally understood as that basis in which the reduced density matrix is driven to a diagonal (classically interpretable) form via environment induced decoherence is addressed. The exact solutions of the Caldeira-Leggett Master Equation are analyzed for a free particle and a harmonic oscillator system. In both cases, we see that the reduced density matrix is driven diagonal in the energy basis, which is momentum for the free particle and the number states for the harmonic oscillator. This seems to single out the energy basis as the preferred basis which is contrary to the general notion that it is the position basis which is selected since the coupling to the environment is via the position coordinates

Controlling wave function localization in a multiple quantum well structure

The dynamics of a wave function describing a particle confined in a multiple quantum well potential is studied numerically. In particular, the case of four wells and six wells has been studied for the first time. As a consequence of quantum mechanical tunneling, an initial wavefunction designed to be localized in one well can localize in the others after a certain time and hop between wells at times which depends on the height and width of the barriers separating the wells. This control over the evolution of the wavefunction with time has direct implications in applications based on carrier dynamics in multiple quantum well nanostructures and can also provide novel mechanisms in solid state quantum computation for information storage and processing. The ability to include any number of wells and control the carrier dynamics in them through easily accessible parameters in our study makes this a particularly attractive system from the point of view of applications.

Preferred states of the apparatus

A simple one-dimensional model for the system–apparatus interaction is analysed. The system is a spin-1/2 particle, and its position and momentum degrees constitute the apparatus. An analysis involving only unitary Schrödinger dynamics illustrates the nature of the correlations established in the system–apparatus entangled state. It is shown that even in the absence of any environment-induced decoherence, or any other measurement model, certain initial states of the apparatus – like localized Gaussian wavepackets – are preferred over others, in terms of measurementlike one-to-one correlations in the pure system–apparatus entangled state.

The coming of a classical world

Quantum theory’s unusual predictions stem from its basic formalism which involves concepts like the wavefunction or probabilityamplitudes instead of probabilities. Many serious doubts have been raised about quantum theory’s connection with perceived classical dynamics. How does quantum mechanics, with all its strange ideas, unfold to give us the ‘reality’ of the familiar physical world? What is the connection between theclassical and thequantum! If quantum mechanics is, indeed, the fundamental theory of nature, as is widely accepted, then how does it explainclassicality! In the following, some of the fascinating conceptual problems of quantum mechanics are highlighted. The ‘environment-induceddecoherence’ approach is then discussed as one practical attempt at explaining the emergence of a classical world from an underlying quantum substrate

Optical mode-coupling in a ring due to a back-scatterer

The coupling of light waves travelling clockwise and counterclockwise along an optical ring due to a back-scattering element is studied. An asymmetric mode splitting occurs as a consequence of the discontinuity suffered by the waves at the scattering point. The mode splitting shows up in an interference pattern and lends itself to an experimental verification.

Monitoring decoherence via measurement of quantum coherence

Abstract A multi-slit interference experiment, with which-way detectors, in the presence of environment induced decoherence, is theoretically analyzed. The effect of environment is modeled via a coupling to a bath of harmonic oscillators. Through an exact analysis, an expression for C , a recently introduced measure of coherence, of the particle at the detecting screen is obtained as a function of the parameters of the environment. It is argued that the effect of decoherence can be quantified using the measured coherence value which lies between zero and one. For the specific case of two slits, it is shown that the decoherence time can be obtained from the measured value of the coherence, C , thus providing a novel way to quantify the effect of decoherence via direct measurement of quantum coherence. This would be of significant value in many current studies that seek to exploit quantum superpositions for quantum information applications and scalable quantum computation.

Wigner Function Description of Nonlocal Features of Quantum Fields Generated in Nonlinear Optical Processes

Fields generated in a large number of nonlinear optical processes (including those with losses) have a Wigner distribution which is Gaussian centered around the mean value of the field.4 We show9 that the Bell inequality for an optical correlation experiment with two coupled modes generated in a nonlinear process can be expressed as an inequality relating to the parameters of the underlying Wigner distribution function. The example of parametric down-conversion, which has already been used in experiments2 to demonstrate the quantum nonlocality, is considered.