Davies theory for reservoir-induced entanglement in a bipartite system

Abstract

Two mutually noninteracting qubits with identical modest coupling to one and the same reservoir are considered. For a given Hamiltonian and uncorrelated initial state, the mathematically rigorous Davies theory of the weak-coupling and van Hove limit provides a unique Markovian quantum master equation where absolutely none of the usually made additional assumptions and further approximations are introduced. Due to completely positive time evolution also no artificial correlations can arise. Numerical solution of the Markovian master equation shows that the qubits become entangled. In a first short time-interval containing one single maximum of entanglement for reservoir temperature T = 0, different choices of uncorrelated initial states give rise to a remarkable emergence of entanglement of different degree. The quantitative evaluation is analysed in terms of a measure derived from Wootters concurrence. Selected results show that there are even states that acquire the possible maximum. Particularly those states will show a periodic type of ‘collapse and revival’ behaviour with exponentially decaying envelope at longer times. This has never been reported so far for noninteracting qubits as mediated by simultaneous coupling to an uncontrollable reservoir. Moreover, even selected uncorrelated mixed states of modest degree of mixture may show a similar behaviour, although less pronounced. For T > 0 states with high degree of entanglement at T = 0 in the first time-interval still show a gradually reduced value up to a few tenth of Kelvin but for T ⩾ 33 K no effects can be observed. Finally, initially entangled states will slowly lose their oscillatory degree, again with exponential envelope, as the bipartite system approaches its stationary final state.

Temperature-independent teleportation of qubits in Davies environments

“…The opposite case, i.e., G = 0 and A = 0, cannot be physically realized as the dissipation of energy is necessarily accompanied by finite dephasing. It is also reflected in the inequality (14). Let us notice that an explicit temperature dependence (via p) of the Davis map Eq.…”

“…They satisfy most of the desired thermodynamic and statistical-mechanical properties such as the detailed balance condition [1]. Davies approximation has recently been applied to studies of various problems in quantum information and physics of open quantum systems including entanglement dynamics [14], quantum discord [7,10], or properties of geometric phases of qubits [8].…”

“…Let us notice that due to the condition Eq. (14), the ordering of limits follows from physical arguments.…”

Quantum correlations as precursors of entanglement

“…This has important consequences for the dynamical behavior of the system. A common environment may entangle initially separable systems, even in the absence of direct interaction [37][38][39][40][41][42][43][44][45][46][47]. This can be easily understood from the fact that the product state |0 |⊗|1 may be expressed as a sum of a singlet and a triplet component:…”

Payoffs and Coherence of a Quantum Two-Player Game in a Thermal Environment

“…with partition function Z = Tre −βH and with inverse temperature β. Davies approximation has been successfully used in studies of various problems in quantum information and physics of open quantum systems, including entanglement dynamics [33,34], quantum discord [35] or properties of geometric phases of qubits [36] and the thermodynamic properties of nano-systems [37]. The main properties of the Davies semigroups is that the unitary part and the dissipative part decouples, and in equilibrium, transition rates between eigenstates of Hamiltonian H obey a micro-reversibility condition, i.e., the transition in one direction is exactly balanced from the opposite one.…”