Entanglement protection via periodic environment resetting in continuous-time quantum-dynamical processes

Abstract

The temporal evolution of entanglement between a noisy system and an ancillary system is analyzed in the context of continuous-time open quantum system dynamics. Focusing on a couple of analytically solvable models for qubit systems, we study how Markovian and non-Markovian characteristics influence the problem, discussing in particular their associated entanglement-breaking regimes. These performances are compared with those one could achieve when the environment of the system is forced to return to its input configuration via periodic instantaneous resetting procedures.

Degradation and Protection of Entanglement in Open Quantum Systems †

“…Therefore entanglement can eventually reach zero at the special times (or time intervals) where the process becomes EB, and then reappear again (see the solid blue line in Figure 2c). In [13] it has been shown that the EB properties of a non-Markovian evolution can be manipulated by properly acting on the environment via periodic resetting of its initial state. This is formally realized by dividing the temporal axis into a collection of time intervals I n = [t n , t n+1 ) of equal length τ = t n+1 − t n with t 0 = 0, and by defining a new family of mappings {Φ Figure 2c we report a case study regarding a qubit S interacting with a bosonic reservoir at zero temperature characterized by a Lorentzian spectral density.…”

Degradation of entanglement in Markovian noise

“…that holds for a generic (time-independent) unitary conjugation U. Equation (19) can be easily verified by noticing that given the semigroup Φ t generated by L, and the semigroup Φ t generated by L = U −1 • L • U, the two are connected as in (18) by setting V t = U −1 and U t = U.…”

“…Since it defines the maximum time interval on which we are guaranteed to have some entanglement between A and B under the evolution (1), we shall refer to τ ent as the "entanglement survival time" (EST) of the selected dynamical process. Notice however that if the maps {Φ t,0 } t≥0 exhibit a strong non-Markovian character inducing a significative back-flow of information into the system temporal evolution [15][16][17][18][19], nothing prevents the possibility that entanglement between A and B will re-emerge at some time t greater than τ ent . The same effect however cannot occur in the case of Markovian or weakly non-Markovian models for which instead one has…”

“…In analogy with the phase-flip process, if we setn = (0, 0, 1) the Hamiltonian part of L can be eliminated by passing into the interaction picture representation, therefore the EST does not depend on ω. Also, exploiting the unitary invariance (19), the azimuthal angle ϕ can be set to 0 without loss of generality, leaving us only with the dependence on θ to be resolved. In Fig.…”

Effect of an incoherent pump on two-mode entanglement in optical parametric generation

“…A general noise results in the purity degradation (the state becomes mixed) and entanglement degradation (the state becomes separable if the noise is strong enough [37,47]). To fight with reasons (i) and (ii), one resorts to the most robust entangled states [37,48] or interventions in the noisy dynamics [49]. Reason (iii) significantly affects the performance of entanglement-enabled protocols because any such protocol relies on a properly prepared (pure) entangled state [1, [25][26][27].…”