Measuring CP violation using quantum state tomography

TL;DR

The paper introduces quantum state tomography as a novel, state-centric method to quantify direct CP violation in neutral meson decays by reconstructing CP-conjugate density matrices across isospin, SU(3) flavor, and helicity spaces and measuring their difference with the trace distance $\mathscr{D}^T(\rho,\bar{\rho})$. It provides explicit constructions for kaon isospin states, scalar octet flavor states, and spin-1 helicity states, connecting CP violation to entanglement, contextuality, and nonlocality in these systems. Across several channels, the trace-distance results yield high-significance evidence of CP violation: kaons $\mathscr{D}^T_{CP}=(1.10\pm0.14)\times10^{-5}$ (7.2$\sigma$), $B$- and $D$-meson flavor octets $\mathscr{D}^T_{CP}=0.11\pm0.02$ (5.5$\sigma$) and $(3.31\pm1.02)\times10^{-3}$ (3.3$\sigma$), and helicity analyses $\mathscr{D}^T_{CP}=0.028\pm0.006$ (4.7$\sigma$) and $0.087\pm0.040$ (2$\sigma$). The method often matches or exceeds traditional asymmetry-based measurements, offering a unifying quantum-information framework for CP studies and motivating extensions to additional decay modes. Overall, the work demonstrates a practical, information-rich approach to characterize CP violation in meson decays with broad applicability.

Abstract

We investigate direct CP violation in neutral meson decays by reconstructing the associated density matrices and measuring their difference using the trace distance. Our results cover neutral kaon decays into two scalar triplets of isospin space, specifically the pions, and decays of $B$- and $D$- mesons into two scalar octets of SU(3) flavor space. We briefly discuss the quantum properties of these states, including entanglement, contextuality, and nonlocality. Additionally, we demonstrate a comparable approach for spin-1 final states by employing a density matrix describing states in the space of helicities. The significance of CP violation obtained through this method is consistently comparable, and often surpasses that obtained using only single, or combinations of, asymmetries.

Figures (1)

• Figure 1.1: Examples of states in flavor space, $\Psi_3$ (left-hand side), and in helicity space, $\Phi$ (right-hand side), together with their CP-conjugated states $\overline \Psi_3$ and $\overline \Phi$. The axes are the bases of the two-dimensional Hilbert spaces: bipartite neutral states in isospin ($|\pi^i\pi^j\rangle$) and helicities ( ($|h_\pm\rangle$)), respectively. The difference between a state and its CP-conjugated partner is measured by the trace distance.