Decoherence of entangled kaons and its connection to entanglement measures

Abstract

We study the time evolution of the entangled kaon system by considering the Liouville -von Neumann equation with an additional term which allows for decoherence. We choose as generators of decoherence the projectors to the 2-particle eigenstates of the Hamiltonian. Then we compare this model with the data of the CPLEAR experiment and find in this way an upper bound on the strength λ of the decoherence. We also relate λ to an effective decoherence parameter ζ considered previously in literature. Finally we discuss our model in the light of different measures of entanglement, i.e. the von Neumann entropy S, the entanglement of formation E and the concurrence C, and we relate the decoherence parameter ζ to the loss of entanglement: 1 − E.

Entanglement, Bell Inequalities and Decoherence in Particle Physics

“…7). This is of special interest in case of entangled states where a single parameter, the decoherence parameter λ or ζ [42,48,36], quantifies the strength of decoherence between the two subsystems or the amount of spontaneous factorization of the wavefunction. The asymmetry of like-and unlike-flavor events is directly sensitive to λ or ζ.…”

“…The increase of decoherence of the initially totally entangled K 0K 0 system as time evolves means on the other hand a decrease of entanglement of the system. This loss of entanglement can be measured explicitly [48,91].…”

“…How possible decoherence might arise from the interaction of the system with its "environment", whatever this may be, and we will determine the strength of such effects. We study how decoherence is related to the loss of entanglement, and pursue the question: how to detect and quantify entanglement [48].…”

“…Proposition: Bertlmann-Durstberger-Hiesmayr [48] • The entanglement loss equals the decoherence ! Therefore we are able to determine experimentally the degree of entanglement of the K 0K 0 system, namely by considering the asymmetry (99) and fitting the parameter ζ or λ to the data.…”

“…Proposition: Bertlmann-Durstberger-Hiesmayr [48] • The state represented by the density matrix ρ N (t) (106), (93) becomes mixed for 0 < t < ∞ but remains entangled. Separability is achieved asymptotically t → ∞ with the weight e −λt .…”