Preservation of quantum coherence under Lorentz boost for narrow uncertainty wave packets

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.

Figure 1

${\rho }_{s12}^{\mathrm{\Lambda }}$ vs $\alpha$ and $\sigma$ (MeV) for wave packet centered at zero.

Figure 2

${\rho }_{s12}^{\mathrm{\Lambda }}$ vs $\alpha$ and $\sigma$ (MeV) for wave packet centered at $\mathfrak{p}$.

Figure 3

$C_{\mathrm{rel}.\mathrm{ent}.}$ vs $\alpha$ and $\sigma$ (MeV) for wave packet centered at zero.

Figure 4

$C_{\mathrm{rel}.\mathrm{ent}.}$ vs $\alpha$ and $\sigma$ (MeV) for wave packet centered at $\mathfrak{p}$.

Figure 5

“Skew information” $\mathcal{I}$ vs $\alpha$ and $\sigma$ (MeV) for wave packet centered at zero.

Figure 6

“Skew information” $\mathcal{I}$ vs $\alpha$ and $\sigma$ (MeV) for wave packet centered at $\mathfrak{p}$.

Figure 7

“Frobenius-norm-based measure of coherence” $C_F$ vs $\alpha$ and $\sigma$ (MeV) for wave packet centered at zero.

Figure 8

“Frobenius-norm-based measure of coherence” $C_F$ vs $\alpha$ and $\sigma$ (MeV) for wave packet centered at $\mathfrak{p}$.

Figure 9

“Frobenius-norm-based measure of coherence” vs $\alpha$ and $\sigma$ (MeV) for narrow uncertainty neutron wave packet.