Erratum: Complete positivity, finite-temperature effects, and additivity of noise for time-local qubit dynamics [Phys. Rev. A 93 , 052103 (2016)]

Abstract

The parameter t 3 (t) in Eq. (20) of the main article should be replaced witht 3 (t), defined as(1)With this change to Eqs. (27) and (28) of the main article, the corrected versions of p(t) and q(t) becomẽrespectively. By applying these corrections to the complete positivity criteria in Eqs. (25) and (26) of the main article one getsSinceỹ(t) andw(t) do not depend ont 3 (t), they are not affected by the correction. By comparing Eqs. (4) and (5) above with the conditions in Eqs. (25) and (26) of the main article, respectively, we see that the corrected and original conditions are equivalent. Thus, we conclude that the correction in t 3 (t) has no effect on the complete positivity criteria studied.2469-9926/2016/94(5)/059904(1) 059904-1

Witnessing non-Markovian effects of quantum processes through Hilbert-Schmidt speed

“…We start by considering a single qubit undergoing a socalled phase covariant noise. The general time-local master equation, in the interaction picture (in units of ), for the density matrix ρ for a single qubit subject to phase-covariant noise is written as [59,66,67]…”

“…where ω(t) represents a time-dependent frequency shift, γ i (t) (i = 1, 2, 3) denotes the time-dependent rate associated to each dissipator L i (ρ), whose expressions are [59]…”

“…Indicating with |0 and |1 the ground and excited states of the qubit, respectively, one can show that the solution of the master equation of Eq. ( 12) is given by [59]…”

“…We check the efficiency of the proposed HSS-based witness in several typical situations of open quantum systems made of qubits and qutrits. In particular, we consider: one qubit subject to phasecovariant noise [59], especially the so-called eternal non-Markovianity model [36,[60][61][62][63]; a single qubit undergoing the Pauli channel [3,60,64]; two independent qubits locally interacting with leaky cavities; V-type and Λ-type three-level atom (qutrit) in a dissipative cavity. We find that the HSSbased non-Markovianity measure identifies memory effects in total agreement with the trace distance-based BLP measure, thus detecting system-environment information backflows.…”

Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket

“…The price one pays for this reduction is highly nontrivial structure of time-dependent rates in the time-local master equation. The corresponding time-local generator is phase covariant and its general properties recently studied providing us with the necessary tools to analyze non-Markovanity effects [28][29][30][31][32][33]. The derived time dependent rates governing damping (cooling), heating and decoherence processes are fully characterized by the wave packet profile.…”