Abstract
Noise sources are ubiquitous in Nature and give rise to a description of quantum systems in terms of stochastic Hamiltonians. Decoherence dominates the noise-averaged dynamics and leads to dephasing and the decay of coherences in the eigenbasis of the fluctuating operator. For energy-diffusion processes stemming from fluctuations of the system Hamiltonian the characteristic decoherence time is shown to be proportional to the heat capacity. We analyze the decoherence dynamics of entangled CFTs and characterize the dynamics of the purity, and logarithmic negativity, that are shown to decay monotonically as a function of time. The converse is true for the quantum Renyi entropies. From the short-time asymptotics of the purity, the decoherence rate is identified and shown to be proportional to the central charge. The fixed point characterizing long times of evolution depends on the presence degeneracies in the energy spectrum. We show how information loss associated with decoherence can be attributed to its leakage to an auxiliary environment and discuss how gravity duals of decoherence dynamics in holographic CFTs looks like in AdS/CFT. We find that the inner horizon region of eternal AdS black hole is highly squeezed due to decoherence.
Highlights
Keeping give rise to fluctuations in the system Hamiltonian [2, 3]
We show how information loss associated with decoherence can be attributed to its leakage to an auxiliary environment and discuss how gravity duals of decoherence dynamics in holographic conformal field theory (CFT) looks like in anti-de Sitter space (AdS)/CFT
We have analyzed the decoherence dynamics induced by energy dephasing in conformal field theories
Summary
For a given set of realizations of these processes {ξtμ}, the dynamics is governed by the stochastic master equation d|Ψξt = − i H0dt|Ψξt − i. Where dWtμ, defined from ξtμ := dWtμ/dt is an Ito stochastic differential. As such, it obeys the relations dWtμdWtν = δμνdt and dWtμdt = dt2 = 0. The noise-averaged dynamics is governed by the master equation i ρ(t) = − [H0, ρ(t)] − 2 γμ [Vμ, [Vμ, ρ(t)]] , μ (2.3). Whenever the fluctuating operator is fully non-local (e.g., a random matrix operator), the decoherence rate becomes proportional to the Hilbert space dimension, and this exhibits an exponential dependence on systems of interacting qubits [20]
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