Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Quantum coherence measures in entangled atomic systems

Arnab Mukherjee, Soham Sen, Sunandan Gangopadhyay

TL;DR

The paper investigates how Lorentz boosts affect quantum coherence in entangled bipartite systems prepared with generalized Gaussian momentum wave packets. Using Wigner-rotations to model spin–momentum coupling, it derives boosted two-particle states for scenarios where one or both particles are boosted and computes $l_1$-norm and Frobenius-norm coherence of the spin reduced states, highlighting dependence on boost parameters, Gaussian width $\sigma$, mass $m$, and the generalization parameter $n$. The main results show that $C_{l_1}$ remains $C_{l_1}(\rho^{R}_{\Lambda})=\sin(2\theta)$ at leading order, while $C_F$ decays as $1-\frac{2n+1}{6}\left(\frac{\cosh\alpha-1}{\cosh\alpha+1}\right)\left(\frac{\sigma}{m}\right)^2$ (and similarly for the two-boost case with $\alpha_1,\alpha_2$), with stronger decoherence when both particles are boosted. Reducing to a single-particle picture reveals that non-maximal entanglement is required to observe Lorentz-boost-induced coherence changes, whereas maximally entangled states can be insensitive in that reduced view. Overall, the work demonstrates a measurable relativistic influence on coherence resources and clarifies how momentum-space structure and entanglement affect their frame dependence.

Abstract

In this study, we investigate the effect of the Lorentz transformation on the measures of quantum coherence in an entangled atomic system. Here, we consider the effect of this relativistic boosts on two-particle entangled generalized Gaussian wave packets in two scenarios. In the first scenario, we consider that the relativistic boost affects the one particle and other remains unaffected while in the second scenario, we consider that both the particles are affected by the effect of the relativistic boost. The coherence of the wave function as measured by the boosted observer is studied as a function of the boost parameter and the width of the Gaussian wave packets. Using various formulations of coherence, it is shown that in general the coherence decays with increase in the width of the Gaussian wave packet, higher values of boost parameter, and the number of particles on which boost is applied.

Quantum coherence measures in entangled atomic systems

TL;DR

The paper investigates how Lorentz boosts affect quantum coherence in entangled bipartite systems prepared with generalized Gaussian momentum wave packets. Using Wigner-rotations to model spin–momentum coupling, it derives boosted two-particle states for scenarios where one or both particles are boosted and computes -norm and Frobenius-norm coherence of the spin reduced states, highlighting dependence on boost parameters, Gaussian width , mass , and the generalization parameter . The main results show that remains at leading order, while decays as (and similarly for the two-boost case with ), with stronger decoherence when both particles are boosted. Reducing to a single-particle picture reveals that non-maximal entanglement is required to observe Lorentz-boost-induced coherence changes, whereas maximally entangled states can be insensitive in that reduced view. Overall, the work demonstrates a measurable relativistic influence on coherence resources and clarifies how momentum-space structure and entanglement affect their frame dependence.

Abstract

In this study, we investigate the effect of the Lorentz transformation on the measures of quantum coherence in an entangled atomic system. Here, we consider the effect of this relativistic boosts on two-particle entangled generalized Gaussian wave packets in two scenarios. In the first scenario, we consider that the relativistic boost affects the one particle and other remains unaffected while in the second scenario, we consider that both the particles are affected by the effect of the relativistic boost. The coherence of the wave function as measured by the boosted observer is studied as a function of the boost parameter and the width of the Gaussian wave packets. Using various formulations of coherence, it is shown that in general the coherence decays with increase in the width of the Gaussian wave packet, higher values of boost parameter, and the number of particles on which boost is applied.

Paper Structure

This paper contains 11 sections, 75 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Single particle quantum state under Lorentz boost
  3. Bipartite quantum state under Lorentz boost
  4. When only one particle is under the Lorentz boost
  5. When both the particles are under the Lorentz boost
  6. Effect of the Lorentz boost on quantum coherence measures
  7. $l_1$ norm measure of coherence
  8. Frobenius-norm measure of coherence
  9. Reduction into a single-particle scenario
  10. Findings
  11. Conclusions

Figures (2)

  • Figure 1: The Frobenius norm measure of coherence, $C(\rho^{R}_\Lambda)$ plotted with the values of the boost parameter $\beta~=~0.95,~0.8,~0.3,~0.0$, with $n=2$.
  • Figure 2: The Frobenius norm measure of coherence, $C(\rho^{R}_{\Lambda_1\Lambda_2})$ plotted with the values of the boost parameter $\beta_1=\beta_2=0.95,~0.8,~0.3,~0.0$, with $n=2$.