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Physical Review A

Controlled measurement processes: Simple spin-chain model of controlled quantum-state amplification

Vinitha Balachandran, Jiangbin Gong

Published Jan 15, 2009• 4 citations
Publisher

Abstract

Controlled measurement processes with high fidelity and robustness will be of substantial interest to fundamental quantum studies as well as quantum-information processing. This work proposes a simple scheme to realize controlled measurements of the state of a single spin, via controlled quantum signal amplification in a one-dimensional spin-chain model. It is shown that, by adiabatically moving an external field applied to a spin chain that is also irradiated with a transverse driving field, a robust spin amplifier may be realized with little dispersion. Our results may find applications in spin-based quantum-information processing and in controlled growth of ``Schr\"odinger cat'' states.

DOI
10.1103/physreva.79.012317

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Controlled measurement processes with high fidelity and robustness will be of substantial interest to fundamental quantum studies as well as quantum-information processing. This work proposes a simple scheme to realize controlled measurements of the state of a single spin, via controlled quantum signal amplification in a one-dimensional spin-chain model. It is shown that, by adiabatically moving an external field applied to a spin chain that is also irradiated with a transverse driving field, a robust spin amplifier may be realized with little dispersion. Our results may find applications in spin-based quantum-information processing and in controlled growth of ``Schr"odinger cat'' states.
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We study the dynamics of a one dimensional quantum spin chain evolving from unentangled or entangled initial state. At a given instant of time a quantum dynamical process (ex. measurement) is performed on a single spin at one end of the chain. The aim is to detect if the process occurred or not from a measurement on a far away spin at a later time. From the dynamical evolution of the state from the epoch time it is possible to detect the occurrence of the dynamical process. The propagation of the signal for the dynamical process, and the speed of the signal are investigated for various spin models, viz. the Ising, Heisenberg, and the transverse-XY dynamics.
This thesis is concerned with finding technologically useful quantum phenomena that are robust against real world imperfections. We examine three different areas covering techniques for spin measurement, photon preparation and error correction. The first research chapter presents a robust spin-measurement procedure, using an amplification approach: the state of the spin is propagated over a two-dimensional array to a point where it can be measured using standard macroscopic state mea- surement techniques. Even in the presence of decoherence, our two-dimensional scheme allows a linear growth in the total spin polarisation - an important increase over the √t obtainable in one-dimension. The work is an example of how simple propagation rules can lead to predictable macroscopic behaviour and the techniques should be applicable in other state propagation schemes. The next chapter is concerned with strategies for obtaining a robust and reliable single photon source. Using a microscopic model of electron-phonon interactions and a quantum master equation, we examine phonon-induced decoherence and assess its impact on the rate of production, and indistinguishability, of single photons emitted from an optically driven quantum dot system. We find that, above a certain threshold of desired indistinguishability, it is possible to mitigate the deleterious effects of phonons by exploiting a three-level Raman process for photon production. We introduce a master equation technique for quantum jump situations that should have wide application in other situations. The final chapter focusses on toric error correcting codes. Toric codes form part of the class of surface codes that have attracted a lot of attention due to their ability to tolerate a high level of errors, using only local operations. We investigate the power of small scale toric codes and determine the minimum size of code necessary for a first experimental demonstration of toric coding power.
Abstract We study the dynamics of a one dimensional quantum spin chain evolving from unentangled or entangled initial state. At a given instant of time a quantum dynamical process (ex. quantum measurement operation) is performed on a single spin at one end of the chain, decohering the system. Through the further unitary evolution, a signal propagates in the spin chain, which can be detected from a measurement on a different spin at later times. From the dynamical unitary evolution of the decohered state from the epoch time, it is possible to detect the occurrence of the quantum operation. The propagation of the signal for the dynamical process, and the speed of the signal are investigated for various spin models, viz. using the Ising, Heisenberg and transverse- XY dynamics.
Control of the transfer of quantum information encoded in quantum wave packets moving along a spin chain is demonstrated. Specifically, based on a relationship with control in a paradigm of quantum chaos, it is shown that wave packets with slow dispersion can automatically emerge from a class of initial superposition states involving only a few spins, and that arbitrary unspecified traveling wave packets can be nondestructively stopped and later relaunched with perfection. The results establish an interesting application of quantum chaos studies in quantum information science.
Propagation of soliton-like excitations along spin chains has been proposed as a possible way for transmitting both classical and quantum information between two distant parties with negligible dispersion and dissipation. In this work, a somewhat different use of solitons is considered. Solitons propagating along a spin chain realize an effective magnetic field, well localized in space and time, which can be exploited as a means to manipulate the state of an external spin (i.e., a qubit) that is weakly coupled to the chain. We have investigated different couplings between the qubit and the chain, as well as different soliton shapes, according to a Heisenberg chain model. It is found that symmetry properties strongly affect the effectiveness of the proposed scheme, and the most suitable setups for implementing single qubit quantum gates are singled out.