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Quantum discord of mixed states under noisy channels in the curved spacetime

Yuxuan Xiong, Zhiling Pi, Tinggui Zhang, Xiaofen Huang

Abstract

We focus our attention on two-qubit mixed states as initial states, and apply the geometric measure of quantum discord to investigate quantum discord properties in the background of a Schwarzschild black hole under phase damping, phase flip and bit flip channels, respectively. Several analytical complementary relationships based on quantum discords for bipartite subsystems are proposed. For the three channel noises, the behaviors of discords are similar, the accessible discords always degrade as the Hawking acceleration rising, but sudden death never occurs, while the inaccessible discords increase from zero monotonically. Interestingly, in the case of the bit flip channel and phase flip channel, the discords perform symmetrically with the decay probability rising.

Quantum discord of mixed states under noisy channels in the curved spacetime

Abstract

We focus our attention on two-qubit mixed states as initial states, and apply the geometric measure of quantum discord to investigate quantum discord properties in the background of a Schwarzschild black hole under phase damping, phase flip and bit flip channels, respectively. Several analytical complementary relationships based on quantum discords for bipartite subsystems are proposed. For the three channel noises, the behaviors of discords are similar, the accessible discords always degrade as the Hawking acceleration rising, but sudden death never occurs, while the inaccessible discords increase from zero monotonically. Interestingly, in the case of the bit flip channel and phase flip channel, the discords perform symmetrically with the decay probability rising.
Paper Structure (5 sections, 34 equations, 4 figures)

This paper contains 5 sections, 34 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Geometric measure of quantum discord under the effect of Hawking radiation
  3. Geometric measure of quantum discord affected by noisy environment
  4. Conclusions
  5. Appendix

Figures (4)

  • Figure 1: Plot quantum discords $D(\rho_{A_{I}B_I})$ , $D(\rho_{A_{I}B_{II}} )$ and $D(\rho_{A_{II}B_{II}} )$ when Hawking acceleration $r_a=r_b=r$ for various state parameters.
  • Figure 2: Plot quantum discords $D(\rho_{A_{I}B_I})$, $D(\rho_{A_{I}B_{II}} )$ and $D(\rho_{A_{II}B_{II}} )$ under phase damping noisy when $r_a=r_b=r$. The upper three subfigures are the cases that discord is a function of acceleration parameter $r$ with several different values of state parameter $p$ for $k=\frac{1}{3}$. The lower three subfigures are the cases that discord is a function of both acceleration parameter $r$ and decay probability parameter $k$.
  • Figure 3: Plot quantum discords $D(\rho_{A_{I}B_I})$, $D(\rho_{A_{I}B_{II}} )$ and $D(\rho_{A_{II}B_{II}} )$ for the phase flip channel when $r_a=r_b=r$. The upper subfigures are the cases that discord is a function of acceleration parameter $r$ for $k=\frac{1}{3}$. The lower subfigures are the cases that discord is a function of both acceleration parameter $r$ and decay probability parameter $k$.
  • Figure 4: Plot quantum discords $D(\rho_{A_{I}B_I})$, $D(\rho_{A_{I}B_{II}} )$ and $D(\rho_{A_{II}B_{II}} )$ for the bit flip channel when $r_a=r_b=r$. The upper subfigures are the cases that discord is a function of acceleration parameter $r$ for $k=\frac{1}{3}$. The lower subfigures are the cases that discord is a function of both acceleration parameter $r$ and decay probability parameter $k$.