Non-Markovian dynamics of quantum discord

Abstract

We evaluate the quantum discord dynamics of two qubits in independent and common non-Markovian environments. We compare the dynamics of entanglement with that of quantum discord. For independent reservoirs the quantum discord vanishes only at discrete instants whereas the entanglement can disappear during a finite time interval. For a common reservoir quantum discord and entanglement can behave very differently with sudden birth of the former but not of the latter. Furthermore, in this case the quantum discord dynamics presents sudden changes in the derivative of its time evolution which is evidenced by the presence of kinks in its behavior at discrete instants of time.

Revisiting Quantum Discord for Two-Qubit X States: The Error Bound to an Analytical Formula

“…Quantum discord for a Bell-diagonal state was analytically obtained [10]. Much research has had a focus on finding the quantum discord of the X state [12][13][14][15][16][17][18].…”

“…al. [14] tried to find an * Electronic address: mslab.nk@gmail.com † Electronic address: yyhkwon@hanyang.com analytic formula of the quantum discord for symmetric X state. Recently, by using von Neumann measurement Y. Huang showed that the result of [12] may be valid with some worst-case error [15].…”

Unified scheme for correlations using linear relative entropy

“…Remark that χ − ρ possesses parity and exchange symmetries. Thus, its closest product state can be obtained using the method leading to the closest product state (32). As result, one gets…”

“…Analytical results are known only in a few families of two-qubit states [27,28,29,30,45,46,47] (see also [48,49] and references therein). The alternative geometric way, proposed in [35], quantifies the quantum discord as the minimal Hilbert-Schmidt distance between a given state ρ and the closest classical states of the form…”

“…Now, it is well understood that almost all quantum states, including unentangled (separable) ones, possess quantum correlations. However, the analytical evaluation of quantum discord requires extremization procedures that can be tedious to achieve [27,28,29,30,31,32,33,34]. To overcome this difficulty, a geometrical approach was proposed in [35].…”