Entanglement entropy in particle decay

Abstract

The decay of a parent particle into two or more daughter particles results in an entangled quantum state as a consequence of conservation laws in the decay process. Recent experiments at Belle and BaBar take advantage of quantum entanglement and the correlations in the time evolution of the product particles to study CP and T violations. If one (or more) of the product particles are not observed, their degrees of freedom are traced out of the pure state density matrix resulting from the decay, leading to a mixed state density matrix and an entanglement entropy. This entropy is a measure of the loss of information present in the original quantum correlations of the entangled state. We use the Wigner-Weisskopf method to construct an approximation to this state that evolves in time in a {\em manifestly unitary} way. We then obtain the entanglement entropy from the reduced density matrix of one of the daughter particles obtained by tracing out the unobserved states, and follow its time evolution. We find that it grows over a time scale determined by the lifetime of the parent particle to a maximum, which when the width of the parent particle is narrow, describes the phase space distribution of maximally entangled Bell-like states. The method is generalized to the case in which the parent particle is described by a wave packet localized in space. Possible experimental avenues to measure the entanglement entropy in the decay of mesons at rest are discussed.Comment: Discussion on wavepackets and experimental measurement. 20 pages, 2 fig

Characterization of Unruh channel in the context of open quantum systems

“…Here, in particular, we study the Unruh effect [10,11,16] which predicts thermal like effects from observing uniform acceleration of the Minkowski vacuum. This has attracted intense interest [17][18][19][20][21][22][23][24][25][26][27] and has emerged as a natural quest in the direction of relativistic quantum information [28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Pre-slow-roll initial conditions: Large scale power suppression and infrared aspects during inflation

“…The details of these methods have been explained in detail in refs. [64,65,79,80] and the reader is referred to these references for details. For self-consistency we give a brief summary of the method in appendix (B).…”

“…[64,65,79,80] where the reader is referred to for a detailed treatment, a brief description is included in appendix (B) for consistency.…”

“…In this appendix, the discussion follows ref. [79,80] where it is shown that the Wigner-Weisskopf approximation and its Markovian implementation maintain unitary time evolution.…”

“…If a parent particle decays into two or more daughter particles, the quantum state that describes the daughter particles is an entangled state [79], the entanglement is a consequence of conservation laws, such as momentum, angular momentum etc. Recently it was recognized that in inflationary cosmology the decay of a particle into sub and superhorizon quanta produces an entangled state with quantum correlations across the Hubble radius [80].…”