Decoherence, discord, and the quantum master equation for cosmological perturbations

Abstract

We examine environmental decoherence of cosmological perturbations in order to study the quantum-to-classical transition and the impact of noise on entanglement during inflation. Given an explicit interaction between the system and environment, we derive a quantum master equation for the reduced density matrix of perturbations, drawing parallels with quantum Brownian motion, where we see the emergence of fluctuation and dissipation terms. Although the master equation is not in Lindblad form, we see how typical solutions exhibit positivity on super-horizon scales, leading to a physically meaningful density matrix. This allows us to write down a Langevin equation with stochastic noise for the classical trajectories which emerge from the quantum system on super-horizon scales. In particular, we find that environmental decoherence increases in strength as modes exit the horizon, with the growth driven essentially by white noise coming from local contribution to environmental correlations. Finally, we use our master equation to quantify the strength of quantum correlations as captured by discord. We show that environmental interactions have a tendency to decrease the size of the discord and that these effects are determined by the relative strength of the expansion rate and interaction rate of the environment. We interpret this in terms of the competing effects of particle creation versus environmental fluctuations, which tend to increase and decrease the discord respectively.

Hot accelerated qubits: decoherence, thermalization, secular growth and reliable late-time predictions

“…for all t. This differential relation is sufficient to justify (1.2), and perturbation theory is then simply used to derive the value of the coefficient Γ. An argument similar in spirit to this -though different in detail -is also often available for computing the late-time limit of open systems [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. We argue here that for many OpenEFT applications it is the Lindblad equation [41,42] that is the desired evolution equation for these purposes.…”

Hot cosmic qubits: late-time de Sitter evolution and critical slowing down

“…Similarities between the physics of quantum systems in gravitational spacetimes (especially with horizons) and open systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] show that this assumption is actually unlikely to be true. The problem is that open systems (by definition) always have an 'environment' whose properties are not measured (in this case, perhaps, the degrees of freedom behind the horizon).…”

Contextual Wavefunction collapse: an integrated theory of quantum measurement

“…The relational interpretation [11,17] argues that the actual values of the physical variables of a system are only meaningful in relation to another system with which this system interacts. Similarly, modal interpretations are not concerned with an objective description independent of observers, but only in consistent classical descriptions of systems that are on a microscopic level described by quantum mechanics [18]. The statistical interpretation [13] suggests that wave functions do not describe single systems but ensembles of identically prepared systems.…”

“…• The quantum to classical transition of quantum perturbations in the inflationary era in the early Universe, leading to classical perturbations on the last scattering surface rather then superpositions of such perturbations [18,[80][81][82], In order to describe this transition, a Lindblad equation is used in [83].…”