Information flow versus divisibility for qubit evolution

Abstract

We study the relation between lack of Information Backflow and completely positive divisibility (CP divisibility) for non-invertible qubit dynamical maps. Recently, these two concepts were shown to be fully equivalent for the so called image non-increasing dynamical maps. Here we show that this equivalence is universal for any qubit dynamical map. A key ingredient in our proof is the observation that there does not exist CPTP projector onto a 3-dimensional subspace spanned by qubit density operators. Our analysis is illustrated by several examples of qubit evolution including also dynamical maps which are not image non-increasing.

Markovianity of an emitter coupled to a structured spin-chain bath

“…For ∆ h further inside the band, the system is more Markovian, in line with a classification based on condition (28), which is closer to being satisfied due to smaller values of the spectral density and its derivative. 69 In the middle of the band (∆ h = 0), until intermediate times, the time dependent |C e | 2 exhibits a monotonic decay, almost exponential, but modulated by oscillations (clearly appreciated in γ vac 3 ) at a frequency approximately equal to 2J (Fig.…”

Observation of information flow in the anti-𝒫𝒯-symmetric system with nuclear spins

“…Therefore, the behavior of the system can be consistently understood and interpreted, whether it is an Hermitian or an anti-PT -symmetric system. In addition, the increase of distinguishability in the broken phase implies that the anti-PT -symmetric system exhibits unique non-Markovian behavior as well [22,23]. To further determine the evolution characteristics, we theoretically calculated the purity of the quantum state in Fig.…”

“…Some relevant experimental demonstrations have been realized in atoms [29][30][31], optical [32][33][34][35][36][37], electrical circuit resonators [38] and diffusive systems [39]. Quantum processes such as symmetry breaking transition, observation of exceptional point and simulation of anti-PT -symmetric Lorentz dynamics have been presented in these experiments [29,33,37,38], whereas the novel characteristics of entanglement [17][18][19] and information flow [22][23][24] in the anti-PT -symmetric system, which would present various phenomena different from Hermitian quantum mechanics and reveal the relationship between system and environment, have not been fully thorough investigated in the experiment.In this work, we propose an algorithm for the simulation of universal anti-PT -symmetric evolution with quantum circuit model and report the first experimental observation of information flow oscillation in anti-PT -symmetric system on Nuclear Magnetic Resonance quantum computing platform. It is based on decomposing the non-Hermitian Hamiltonian evolution into a sum of unitary operators and realizing the simulation in an enlarged Hilbert space with ancillary qubits [40].…”

Entanglement negativity as a universal non-Markovianity witness

“…which must now be valid for all t ≥ 0, all bipartite system-ancilla initial states ρ 1 , ρ 2 and all probabilities p 1 + p 2 = 1 [19]. In this Letter, we will consider evolutions for which this equivalence holds, what in fact includes also all qubit dynamics [20]. That is why, from now on we will refer to non-Markovianity as defined by the violation of CP-divisibility.…”