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Aleph UCLA Undergraduate Research Journal for the Humanities and Social Sciences

A Study of the Dynamics of Quantum Correlations

Patrice A. Camati

Published Apr 24, 2014• 0 citations
OpenAlex

Abstract

In this work, we present an introduction to the quantum information theory. Before dealing with quantum information we develop some necessary tools, the classical information theory and some important concepts in quantum dynamics. We de?ne measures of quantum correlations, concurrence and quantum discord, and study their dynamical evolution when the coupling between the system and environment is considered random. We conclude that a random environment imposes permanent loss of correlations to the system

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In this work, we present an introduction to the quantum information theory. Before dealing with quantum information we develop some necessary tools, the classical information theory and some important concepts in quantum dynamics. We de?ne measures of quantum correlations, concurrence and quantum discord, and study their dynamical evolution when the coupling between the system and environment is considered random. We conclude that a random environment imposes permanent loss of correlations to the system
In this didactic article we explore the concept of quantum correlations beyond entanglement. We begin by introducing and motivating the classically correlated states and then showing how to quantify the quantum correlations using an entropic approach, arriving at a well known measure called the quantum discord. Quantum correlations and discord are then operationally linked with the task of local broadcasting. We conclude by providing some alternative perspectives on quantum correlations and how to measure them.
Knowledge of the dynamical behavior of correlations with no classical counterpart, like entanglement, nonlocal correlations and quantum discord, in open quantum systems is of primary interest because of the possibility to exploit these correlations for quantum information tasks. Here we review some of the most recent results on the dynamics of correlations in bipartite systems embedded in non-Markovian environments that, with their memory effects, influence in a relevant way the system dynamics and appear to be more fundamental than the Markovian ones for practical purposes. Firstly, we review the phenomenon of entanglement revivals in a two-qubit system for both independent environments and a common environment. We then consider the dynamics of quantum discord in non-Markovian dephasing channel and briefly discuss the occurrence of revivals of quantum correlations in classical environments.
Here we provide the contributions' abstracts published in a volume we edited as a special issue in International Journal of Modern Physics B. The volume deals with the recent progress in quantifying quantum correlations beyond the generic notion of 'correlations in a quantum system'. The main goal of the special issue is to provide authoritative reviews on selected topics discussed in the field in the last few years. Nevertheless many articles contain significant original research. The opening section of the issue is dedicated to foundational aspects of quantum mechanics. The second section deals with diverse quantum information insights into the analysis of quantum resources (like entanglement and quantum discord). Many of the concepts presented in the first part of the issue are applied to spin systems in the third section. The last section of the issue is focused on the dynamics of quantum discord in open systems and in quantum communication protocols.
In this work, we study quantum correlations in mixed states. The states studied are modeled by a two-qubit system interacting with its environment via a quantum non demolition (purely dephasing) as well as dissipative type of interaction. The entanglement dynamics of this two qubit system is analyzed. We make a comparative study of various measures of quantum correlations, like Concurrence, Bell's inequality, Discord and Teleportation fidelity, on these states, generated by the above evolutions. We classify these evoluted states on basis of various dynamical parameters like bath squeezing parameter rrr, inter-qubit spacing r12r_{12}r12​, temperature TTT and time of system-bath evolution ttt. In this study, in addition we report the existence of entangled states which do not violate Bell's inequality, but can still be useful as a potential resource for teleportation. Moreover we study the dynamics of quantum as well as classical correlation in presence of dissipative coherence.
In this work, we study quantum correlations in mixed states. The states studied are modeled by a two-qubit system interacting with its environment via a quantum non demolition (purely dephasing) as well as dissipative type of interaction. The entanglement dynamics of this two qubit system is analyzed. We make a comparative study of various measures of quantum correlations, like Concurrence, Bell's inequality, Discord and Teleportation fidelity, on these states, generated by the above evolutions. We classify these evoluted states on basis of various dynamical parameters like bath squeezing parameter rrr, inter-qubit spacing r12r_{12}r12​, temperature TTT and time of system-bath evolution ttt. In this study, in addition we report the existence of entangled states which do not violate Bell's inequality, but can still be useful as a potential resource for teleportation. Moreover we study the dynamics of quantum as well as classical correlation in presence of dissipative coherence.
Correlations are a very important tool in the study of multipartite systems, for both classical and quantum ones. The discussion about the quantum nature of correlations permeates Physics since Einstein, Podolski and Rosen published their famous article criticizing quantum mechanics. Here, we provide a short review about the quantum nature of correlations, discussing both its theoretical and experimental aspects. We focus on quantum discord and related measures. After discussing their fundamental aspects (theoretically and experimentally), we proceed by analysing the dynamical behavior of correlations under decoherence as well as some applications in different scenarios, such as quantum computation and relativity, passing through critical and biological systems.