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arXiv:2511.20371

Quantum coherence measures in entangled atomic systems

Arnab Mukherjee, Soham Sen, Sunandan Gangopadhyay

quant-phSubmitted Nov 25, 2025• Announced Nov 26, 2025• 0 citations
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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.

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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.
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We consider the effect of relativistic boosts on single-particle Gaussian wave packets. The coherence of the wave function as measured by the boosted observer is studied as a function of the momentum and the boost parameter. Using various formulations of coherence, it is shown that in general the coherence decays with the increase of the momentum of the state, as well as the boost applied to it. Employing a basis-independent formulation, we show, however, that coherence may be preserved even for large boosts applied on narrow uncertainty wave packets. Our result is exemplified quantitatively for practically realizable neutron wave functions.
Abstract We describe in this paper the effects of Lorentz boost on the quantum entanglement encoded in two-particle Dirac bispinor Bell-like states. Each particle composing the system described in this formalism has three degrees of freedom: spin, chirality, and momentum, and the joint state can be interpreted as a 6 qubit state. Given the transformation law of bispinor under boosts, we compute the change of the Meyer-Wallach global measure of quantum entanglement due to the frame transformation and study its equivalence to the results obtained for the relativistic spin 1/2 Bell-like states, constructed in the framework of the irreducible representations of the Lorentz group. We verify that the monotonic increase of the global entanglement under boosts for ultra-relativistic states is solely due to an increasing of the entanglement associated with the spins subsystems. For such ultra-relativistic states, the entanglement related to the chirality degrees of freedom is invariant, and the variation of the global entanglement of bispinor states is the same as the one calculated for relativistic spin 1/2 states. We also show that the particle-particle entanglement is invariant under boosts for any Bell-like state.
One of the defining features of quantum theory is entanglement, the notion that quantum systems can display correlations that are impossible from the classical \npoint of view. In quantum information theory entanglement has come to be recognised as a physical resource that enables new technologies that perform information \nprocessing tasks which are beyond the limits of the classical realm. It has been realised only recently that entanglement is dependent on the frame of reference in \nboth inertial and accelerated systems. In this thesis, we investigate the relativistic entanglement of massive spin-1=2 particles in inertial frames by focussing on the \ndependence of entanglement on the geometry of the underlying boost scenario. We first explore the ‘qubit’ of the relativistic setting: a single particle with spin and momentum, with momentum given by a Gaussian distribution. We study the system in a variety of different boost scenarios, analysing the behaviour of entanglement \nfrom a geometric point of view. The spin-spin entanglement of two particle systems is then surveyed for many different discrete product and entangled momenta, with the spins in the Werner state. We also extend the analysis to continuous momentum states and study them in a variety of geometries. The results obtained from the analysis of discrete states are applied to continuous states, leading to a better \nunderstanding of the behaviour of entanglement. We lastly discuss the common view according to which Lorentz boosts leave the total entanglement of the state invariant.
Lorentz boosts applied to particles with spin and momentum degrees of freedom induce momentum-dependent rotations. As, in general, different particles have different momenta, the transformation of the whole state is not a representation of the rotation group. Here we identify the group that acts on a two-particle system and, for the case where the momenta of the particles are correlated, find invariant subspaces that have interesting properties for quantum information processes in relativistic scenarios. A basis of states for the study of transformations of spin states under Lorentz boosts is proposed, which is a good candidate for use in building quantum communication protocols in relativistic scenarios.
To understand the characteristics of quantum entanglement of massive particles under Lorentz boost, we first introduce a relevant relativistic spin observable, and evaluate its expectation values for the Bell states under Lorentz boost. Then we show that maximal violation of the Bell's inequality can be achieved by properly adjusting the directions of the spin measurement even in a relativistically moving inertial frame. Based on this we infer that the entanglement information is preserved under Lorentz boost as a form of correlation information determined by the transformation characteristic of the Bell state in use.