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Quantifying Decoherence

Mohd Shoaib Qureshi, Tabish Qureshi

TL;DR

The paper addresses how to quantify decoherence by linking it to entanglement between a quantum system and its environment across finite and continuous variables.It introduces a simple, normalized measure De derived from the reduced density matrix, applicable as De = (n/(n−1))[1 − Tr(ρ^2)] for finite dimensions and De = 1 − Tr(ρ^2) for continuous variables, with extensions via generalized entanglement measures.The authors derive explicit expressions in several models, including a qubit with a spin-1/2 environment, the spin-boson model, a free particle, and a Stern–Gerlach setup, showing De → 1 in the appropriate limits and providing decoherence time-scales.They also propose a feasible Mach–Zehnder interferometer scheme to measure decoherence experimentally, and emphasize that the measure is basis-independent and not tied to pointer states.

Abstract

Quantum decoherence refers to the phenomenon when the interaction of a quantum system with its environment results in the degradation of quantum coherence. Decoherence is considered to be the most popular mechanism responsible for the emergence of classicality from quantum mechanics. The issue of formulating a measure of decoherence is addressed here. The approach taken here is that decoherence results from the entanglement of a quantum system with certain environment degrees of freedom, and quantifying this entanglement should yield the most natural measure of decoherence. A simple measure of decoherence is presented based on this notion, and it is examined for various example systems. The measure proves to be effective and is relatively straightforward to compute. In addition, a method has been proposed to measure decoherence in a Mach-Zehnder interferometer.

Quantifying Decoherence

TL;DR

The paper addresses how to quantify decoherence by linking it to entanglement between a quantum system and its environment across finite and continuous variables.It introduces a simple, normalized measure De derived from the reduced density matrix, applicable as De = (n/(n−1))[1 − Tr(ρ^2)] for finite dimensions and De = 1 − Tr(ρ^2) for continuous variables, with extensions via generalized entanglement measures.The authors derive explicit expressions in several models, including a qubit with a spin-1/2 environment, the spin-boson model, a free particle, and a Stern–Gerlach setup, showing De → 1 in the appropriate limits and providing decoherence time-scales.They also propose a feasible Mach–Zehnder interferometer scheme to measure decoherence experimentally, and emphasize that the measure is basis-independent and not tied to pointer states.

Abstract

Quantum decoherence refers to the phenomenon when the interaction of a quantum system with its environment results in the degradation of quantum coherence. Decoherence is considered to be the most popular mechanism responsible for the emergence of classicality from quantum mechanics. The issue of formulating a measure of decoherence is addressed here. The approach taken here is that decoherence results from the entanglement of a quantum system with certain environment degrees of freedom, and quantifying this entanglement should yield the most natural measure of decoherence. A simple measure of decoherence is presented based on this notion, and it is examined for various example systems. The measure proves to be effective and is relatively straightforward to compute. In addition, a method has been proposed to measure decoherence in a Mach-Zehnder interferometer.
Paper Structure (12 sections, 50 equations, 3 figures)

This paper contains 12 sections, 50 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Decoherence in a nutshell
  3. Quantifying decoherence via entanglement
  4. Entanglement between the system and environment
  5. A qubit coupled to environment of spin-1/2
  6. Decoherence in the spin-boson model
  7. Quantifying decoherence for continuous variable systems
  8. Generalized entanglement measure and decoherence
  9. Decoherence of a free particle
  10. Decoherence in a Stern-Gerlach experiment
  11. Measuring decoherence
  12. Discussion and conclusions

Figures (3)

  • Figure 1: The decoherence measure $\mathcal{D}_e$ given by (\ref{['Decwave']}), plotted against $t/\tau_D$ for a free particle undergoing decoherence, which is initially in a plane wave state.
  • Figure 2: The decoherence measure $\mathcal{D}_e$ given by (\ref{['Decgauss2']}), plotted against $t/\tau_D$ for a free particle undergoing decoherence, which is initially in a plane wave state.
  • Figure 3: A schematic diagram of a Mach-Zehnder interferometer. The quanton, as it traverses the two paths, may undergo decoherence as a result of interaction with the environment.