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Collective Dynamics in NMR and Quantum Noise

Razieh Annabestani

Published Oct 17, 2016• 0 citations

Abstract

We introduced an open quantum system model to describe the statistical fluctuations of a spin ensemble in NMR. The model considers an ensemble measurement where the detection coil does not distinguish spins, and accounts for the state update rule. The analysis brings clarity and accuracy in describing the notion of spin noise and derives a correct statistical distribution and correlation function for the spin noise signal. \n \nWe propose a proof-of-principle experiment to encode one logical qubit in the noise protected subspace of three identical spins in a methyl group. We use a symmetry analysis to derive the dipole moment allowed transitions, which enable us to access the noiseless subsystem. We fur- ther analyze the symmetry of the hetronuclear dipolar relaxation, which is one of the responsible mechanisms for observing a noise protected state. Our analytical calculations predict features of of the NMR peaks that are in agreement with the experimental observations. \n \nWe propose a quantum key distribution protocol that simplifies the task of classical data processing in a trusted relay network. A new announcement strategy is proposed which leads to reassigning the task of error correction and privacy amplification from the intermediate user to the end-node users. We examine the security of the proposed protocol analytically, derive the key rate for two well-known examples of BB84 and 6-state protocols numerically, and consider a few imperfections arising in practical QKD.

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This thesis examines the security of performing quantum key distribution (QKD) with a simplified trusted relay (STR). The protocol carries out the quantum phase of a conventional trusted relay, however, reduces the required complexity of the nodes by carrying out an altered classical phase. Rather than announcing the parity of the final keys, the simplified trusted relay announces the parity of the keys before error correction and privacy amplification. As a result, the majority of the post-processing is left to the end users. \n \nSpecifically, we examine the security of an STR protocol which carries out the quantum phase of the BB84 protocol. Through two different methods, we derive qubit key rates. For the first method, we require that the basis choice is equally weighted. Furthermore, we limit the relay to a single node. This proof has the benefit that it easily generalizes to an alternate protocol where a node may generate error correcting information. In the second security proof, we derive a key rate for an arbitrary number of nodes with an arbitrary basis weighting. \n \nWe further extend our analysis to realistic scenarios in which the legitimate parties use weak coherent pulses to transmit signal states over a lossy channel. We provide a framework for generalizing decoy state methods to STR protocols.

We propose a proof-of-principle experiment to encode one logical qubit in noise protected subspace of three identical spins in a methyl group. The symmetry analysis of the wavefunction shows that this fermionic system exhibits a symmetry correlation between the spatial degree of freedom and the spin degree of freedom. We show that one can use this correlation to populate the noiseless subsystem by relying on the interaction between the electric dipole moment of the methyl group with a circularly polarized microwave field. Logical gates are implemented by controlling both the intensity and phase of the applied field.