Arbitrary-length XX spin chains boundary-driven by non-Markovian environments

Assessment of the degree of non-Markovianity of open quantum systems and the necessary generalization of quantum state distance measures

“…Again, for the Ohmicdamped case, the dynamics of the first qubit population (Fig. 4(d)) bears strong similarity to the Markoviandamped chain, with a rather unexpected exception, in that the oscillations are found to collapse abruptly after a finite time, a behaviour that has been also reported in previous works involving qubits coupled to Ohmic reservoirs [16,51].…”

“…To address this difficulty, we have developed a formulation enabling the calculation of the amplitudes of the wavefunction of the open system, from which we then construct its density matrix. This formulation has been described in detail in a previous paper [16], where it was used to calculate aspects of the dynamics of a XX chain boundary-driven by non-Markovian environments. As demonstrated below, one of the advantages of this approach is its applicability to any possible form of environmental spectral density, as well as an arbitrary number of qubits in the chain.…”

“…the density matrix of the chain with the last qubit interacting with a non-Markovian reservoir, is a subtler task because the memory effects of the reservoir make the equation of the last qubit amplitude more complicated. In two of our recent papers, we examined the dynamics of XX chain boundary driven by non-Markovian reservoirs [16], as well as the connection between exceptional points and the Quantum Zeno effect in a simpler quantum system consisting of two interacting qubits one of which is coupled to a non-Markovian reservoir [45]. On the basis of the formulation developed in those papers, as applied to the present system, we outline here the basic procedure to obtain the amplitudes of the chain sites.…”

“…Taking the Laplace transform of Eqns. (20) and following the procedure presented in [16] we find that the Laplace transform F 1 (s) of the tilde amplitude c 1 (t) is given by the expression:…”

“…The advantage of our system stems from the combination of a realistic arrangement of an XX chain of qubits, coupled to each other, with one end coupled to a reservoir. In our previous paper [16], we had considered a chain coupled to reservoirs at both ends. Although the present quantitative study could as easily address that arrangement, since our objective is the comparative study of non-Markovian reservoirs, we have chosen to consider the same system with only one end qubit coupled to a variety of reservoirs.…”