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arXiv:quant-ph/0504006

On the KK system as two-kaons system

Jaroslav Hrubý

Published Apr 1, 2005• 0 citations
arXivHTMLPDF

Abstract

The time evolution of the KK system as a two-qubit system is given. The effect which is interpreted as CP violation in neutral kaon decays is explained via violation of quantum correlations during time evolution of the KK system as two-kaons system and description is via Yang-Baxterization and unitary time dependent R-matrices to con- struct Hamiltonian, determining the time evolution of two-kaons sys- tem. The nonseparability ideas and criterion can be extended on all mixing state-antistate system and all CP violation cases in particle physics.

DOI
10.48550/arxiv.quant-ph/0504006

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The time evolution of the KK system as a two-qubit system is given. The effect which is interpreted as CP violation in neutral kaon decays is explained via violation of quantum correlations during time evolution of the KK system as two-kaons system and description is via Yang-Baxterization and unitary time dependent R-matrices to con- struct Hamiltonian, determining the time evolution of two-kaons sys- tem. The nonseparability ideas and criterion can be extended on all mixing state-antistate system and all CP violation cases in particle physics.
The neutral Kaon system has both CP violation in the mass matrix and a non-vanishing lifetime difference in the width matrix. This leads to an effective Hamiltonian which is not a normal operator, with incompatible (non-commuting) masses and widths. In the Weisskopf-Wigner Approach (WWA), by diagonalizing the entire Hamiltonian, the unphysical non-orthogonal "stationary" states KL,SK_{L,S}KL,S​ are obtained. These states have complex eigenvalues whose real (imaginary) part does not coincide with the eigenvalues of the mass (width) matrix. In this work we describe the system as an open Lindblad-type quantum mechanical system due to Kaon decays. This approach, in terms of density matrices for initial and final states, provides a consistent probabilistic description, avoiding the standard problems because the width matrix becomes a composite operator not included in the Hamiltonian. We consider the dominant-decay channel to two pions, so that one of the Kaon states with definite lifetime becomes stable. This new approach provides results for the time dependent decay rates in agreement with those of the WWA.
The study and characterisation of quantum entanglement represents an extended effort within the field of quantum information. This thesis addresses two problems. The first regards entanglement in open systems, where it’s more difficult to define a dichotomic (two outcome) observable due to population loss. The second problem concerns genuine multipartite entanglement, that is entanglement between many particles in states that cannot be separable with respect to any possible bipartition of a system.\nThe first chapter consists of an introduction to the basic elements of quantum mechanics and quantum information theory. We briefly describe a few historical facts about quantum mechanics and the study of entanglement, to help put things into perspective.\nThe second chapter is a detailed discussion of the neutral kaon system. These particles are produced in pairs and are described as a particle-antiparticle system. This system displays some unique properties like the violation of CP-symmetry, and shares some characteristics with other mesons, such as neutral particle oscillation and decay. This makes formulating Bell-type inequalities for them more difficult, but also provides the opportunity for new tests.\nThe third chapter continues with the presentation of an already existent effective formalism for performing Bell tests on neutral kaons. The essence of the formalism is a switch to the Heisenberg picture, transferring the time evolution and dependence on measurement directions to a so-called effective operator. This has many advantages, some of the most important being a proper normalization during population loss (due to decay), an easy application to\nthe case of multiple particles and the fact that it allows one to observe entanglement within the system for a relatively long amount of time. The final part presents a way to simulate neutral kaons with atomic systems, namely with Ytterbium isotopes and discuss what are the differences between these atomic systems and neutral kaons.\nThe second part of the thesis treats the problem of proving genuine multipartite entanglement from separable two-body marginals. For this, an introduction to semidefinite programming is necessary due to the fact that the problem under study can be formulated in terms of this method. We will briefly discuss linear and semidefinite programming as well as the concept of duality and provide some basic examples.\nThe formal description of this problem and previous results are provided in the fifth chapter. Our result shows that, through a cyclic iteration between two SDPs, one obtains states with the desired properties. Using this method we managed to go up to six qubit states for various configurations. From this we can construct higher-dimensional states having the same properties.
The Einstein-Podolsky-Rosen (EPR) entanglement of a neutral K-meson (kaon) pair enjoys the peculiar quantum behaviour of mixing, charge-parity CP{\cal CP}CP violation (C{\cal C}C - charge conjugation, P{\cal P}P - parity) and two non-orthogonal eigenstates of definite time evolution KLK_LKL​ and KSK_SKS​ with very different lifetimes. The dynamics of this strange entanglement, experimentally accessible at the ϕ\phiϕ-factory, makes possible the search for novel phenomena not accessible in any other system, i.e. at interference times and at decoherence times of the single partners after their disentanglement, in order to unveil the nature of the correlation between the two neutral kaons. Until now, the studies have been concentrated on the single kaon intensity distribution between the two decay times t1t_1t1​ and t2t_2t2​ with Δt=t2−t1>0\Delta t = t_2 - t_1 > 0Δt=t2​−t1​>0. Here we show that the entire two single time distributions, before each decay, are physical in both senses: past to future, leading to the state of the living partner at time t2t_2t2​ from the observation of the first decay channel at t1t_1t1​, and future to past, leading to the past state of the decayed kaon at time t1t_1t1​ from the observation of the second decay channel at t2t_2t2​. Our results thus demonstrate an affirmative answer to the title: it does, the past decayed state depends on the result of the future measurement for the living partner. This novel effect is truly observable through the first decay time distributions. Besides the implications for quantum physics for all Δt\Delta tΔt, at large decoherence times the resulting first decayed state is always KSK_SKS​, providing a genuine tag of this kaon state in the decoherence region, and a unique and important experimental tool to prepare a pure KSK_SKS​ beam.
In light of recent exciting progress in building up quantum computing facilities based on both optical and cold-atom techniques, the algorithms for quantum simulations of particle-physics systems are in rapid progress. In this paper, we propose an efficient algorithm for simulating the non-unitary time evolution of neutral-kaon oscillations K0↔K‾0K^0 \leftrightarrow \overline{K}^0K0↔K0, with or without CP conservation, on the quantum computers provided by the IBM company. The essential strategy is to realize the time-evolution operator with basic quantum gates and an extra qubit corresponding to some external environment. The final results are well consistent with theoretical expectations, and the algorithm can also be applied to open systems beyond elementary particles.