Exploiting Gaussian steering to probe non-Markovianity due to the interaction with a structured environment

Ancillary Gaussian modes activate the potential to witness non-Markovianity

“…Analogously to the classical noise channel, we first consider a two-mode state σ AB , where Alice's share undergoes the dynamical map (τ (t)I, η(t)I). [28] uses such a setting to witness non-Markovianity of the channel in the context of quantum Brownian motion-where the initial state is σ AB = σ 2,r . In several scenarios this technique allows to witness non-Markovianity via Gaussian steerability backflows.…”

“…canceling the fast oscillating counter-rotating terms exp(±i2ω 0 t), neglecting the Lamb shift and assuming the environment to be in the thermal state with temperature T, the above equation reduces to the quantum Brownian motion master equation (see e.g. [28,47] with ∆(t) and γ(t) being the diffusion and damping coefficients, respectively, defined in (28) and J(ω) = k g 2 k δ(ω − ω k ) is the spectral density (in the main text, assumed to be of the form (29)). This implies the following master equation for the where we assumed only the first mode to be affected from the channel.…”

“…Gaussian steerability is a form of quantum correlations and, similarly to other correlation measures, is non-increasing under the action of CPTP local maps. For instance, it means that if one is interested in a single mode dynamical channel (T t , N t ), one can construct a local evolution as in (12) and Gaussian steerability can be considered as an information quantifier and used to witness non-Markovianity through backflows, as suggested in [28]. There, the authors show that σ AB (0) = σ 2,r can be deployed as initial state to witness non-Markovianity for the quantum Brownian motion model-see the description in section 5.…”

“…Even less is known for continuous-variable systems and, in particular, for Gaussian dynamics, despite their prominent role in many physically relevant scenarios. While for finite-dimensional, several works have studied correlation backflows in quantum evolutions [25,26,29], continuous-variable settings have not been explored beyond the use of a single ancillary mode [27,28,30].…”

“…Various strategies have been adopted to connect this mathematical definition to more physically motivated ones. This has lead to the development of witnesses of non-Markovianity through backflows of different quantities, such as the error probability in state discrimination [16][17][18], channel capacity [7], Fisher information [19,20], the volume of accessible states [21] and correlations [22][23][24][25][26][27][28]. In the case of correlations, the standard method for witnessing non-Markovianity works as follows: (a) prepare an initial state of two particles, which we name system and ancilla; (b) apply the considered evolution to one of the two particles, the system, while the ancilla remains untouched and (c) monitor how the correlations between the two particles change during the evolution.…”