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Journal of High Energy Physics

Measuring CP violation using quantum state tomography

Marco E. Fabbrichesi, Roberto Floreanini B, Emidio Gabrielli A, Luca Marzola

Published Jul 21, 2026• 0 citations
Publisher

Abstract

A bstract 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.

DOI
10.1007/jhep07(2026)176

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Journal of Physics Conference Series•Jul 1, 2017•0 citations
A bstract 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.
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 BBB- and DDD- 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.
Genuine tests of an asymmetry under T and/or CPT transformations imply the interchange between in-states and out-states. I explain a methodology to perform model-independent separate measurements of the three CP, T and CPT symmetry violations for transitions involving the decay of the neutral meson systems in B- and Φ-factories. It makes use of the quantum-mechanical entanglement only, for which the individual state of each neutral meson is not defined before the decay of its orthogonal partner. The final proof of the independence of the three asymmetries is that no other theoretical ingredient is involved and that the event sample corresponding to each case is different from the other two. The experimental analysis for the measurements of these three asymmetries as function of the time interval Δt > 0 between the first and second decays is discussed, as well as the significance of the expected results. In particular, one may advance a first observation of true, direct, evidence of Time-Reserval-Violation in B-factories by many standard deviations from zero, without any reference to, and independent of, CP-Violation. In some quantum gravity framework the CPT-transformation is ill-defined, so there is a resulting loss of particle-antiparticle identity. This mechanism induces a breaking of the EPR correlation in the entanglement imposed by Bose statistics to the neutral meson system, the so-called ω -effect. I present results and prospects for the ω -parameter in the correlated neutral meson-antimeson states.
We show that two- and three-pion states produced in the decay of neutral kaons are contextual, entangled, and Bell nonlocal in isospin space. By reinterpreting the experimental values of the different isospin amplitudes, we can determine the amount of entanglement enjoyed by these states and the extent to which they violate the noncontextuality and Bell locality inequalities. Notably, the two-pion case provides an example of a state that is more Bell nonlocal, as witnessed by the Collins-Gisin-Linden-Massar-Popescu inequality, than the maximally entangled one. The three-pion state offers a genuine multipartite test of Bell nonlocality with qutrits. This is the first instance where quantum properties like entanglement and contextuality are demonstrated to exist within the internal space of isospin.
Symmetries, and Symmetry Breakings, in the Laws of Physics play a crucial role in Fundamental Science. Parity and Charge Conjugation Violations prompted the consideration of Chiral Fields in the construction of the Standard Model, whereas CP-Violation needed at least three families of Quarks leading to Flavour Physics. In this Lecture I will discuss the Conceptual Basis and the present experimental results for a Direct Evidence of Separate Reversal-in-Time T, CP and CPT Genuine Asymmetries in Decaying Particles like Neutral Meson Transitions, using Quantum Entanglement and the Decay as a Filtering Measurement. The eight transitions associated to the Flavour-CP eigenstate decay products of entangled neutral mesons have demonstrated with impressive significance a separate evidence of TRV and CPV in B d -physics, whereas a CPTV asymmetry shows a 2-σ effect interpreted as an upper limit. Novel CPTV observables are discussed for K and B d transitions. Their observation would lead to a change of paradigm beyond Quantum Field Theory, however there is nothing in Quantum Mechanics forbidding CPTV. A clean methodology to disentangle CPTV effects in the Hamiltonian dynamics and the ω-effect weakening Entanglement in a given experiment is discussed.
The flavor space of particles produced in collider environments contains informative quantum correlations. We present a systematic approach for constructing the complete flavor density matrix for a meson and antimeson system (MM[over ¯]) in the Bloch vector space at a given time t, which can be at or after production. We point out that the B_{s}^{0} and K^{0} systems are superior to the B_{d}^{0} and D^{0} systems for quantum tomography because of their flavor oscillation and decay properties. Performing quantum tomography for the MM[over ¯] system can facilitate the study of production mechanisms, decoherence phenomena, quantum information variables, and potential new sources of CP violation.
We establish the precise connection between the theoretical T, CP, CPT asymmetries, in terms of transition probabilities between the neutral meson B d states, and the experimental asymmetries, in terms of the double decay rate intensities for Flavour-CP eigenstate decay products in a B-Factory of entangled states. Genuine asymmetry parameters in the time distribution of the asymmetries are identified and their measurability analysed, disentangling genuine and possible fake terms. The nine asymmetry parameters – three different observables for each one of the three symmetries – are expressed in terms of the ingredients of the Weisskopf-Wigner dynamical description of the entangled B d -meson states and we obtain a global fit to their values from the BaBar Collaboration experimental results. The possible fake terms are all compatible with zero. The information content of the nine asymmetry parameters is indeed different. The non-vanishing and are impressive separate direct evidence of Time-Reversal-Violation and CP-Violation in these transitions (and compatible with Standard Model expectations). A 2σ effect for the Re(θ) parameter responsible of CPT-Violation appears; interpreted as an upper limit, it leads to eV at 95% C.L. for the diagonal flavour terms of the mass matrix. Finally, we consider scenarios where, in the presence of quantum gravity fluctuations (space-time foam), the CPT operator may be ill-defined. Its perturbative treatment leads to a modification of the Einstein-Podolsky-Rosen correlation of the neutral meson system by adding an Entanglement-weakening term of the wrong exchange symmetry, the ω -effect. The analysis is extended to identify how to probe the complex ω when the connection between the Intensities for the two time-ordered decays ( f, g ) and ( g, f ) is lost ( f flavour and g CP eigenstate decay channels), and how the ω -effect is disentangled from CPT violation in the evolution Hamiltonian.