Anomalous decay of quantum correlations of quantum-dot qubits

Abstract

We study the evolution of quantum correlations, quantified by the geometric discord, of two excitonic quantum dot qubits under the influence of the phonon environment. We show that the decay of these correlations differs substantially form the decay of entanglement. Instead of displaying sudden death type behavior, the geometric discord shows a tendency to undergo transitions between different types of decay, is sensitive to non-local phase factors, and may already be enhanced by weak environment-mediated interactions. Hence, two-qubit quantum correlations are more robust under decoherence processes, while showing a richer and more complex spectrum of behavior under unitary and non-unitary evolution.PACS numbers: 03.65. Ta, 63.20.Kd, 78.67.Hc The study of quantum correlations in realistic systems has, for a long time, been limited to the study of entanglement, due to the fact that straightforward methods of calculating the amount of correlations in a two-qubit system have only been available for some entanglement measures, such as the concurrence [1,2] or negativity [3,4]. Although entanglement itself is a very important resource for a number of applications [5], including quantum computation, quantum cryptography, or teleportation, separability (the lack of entanglement) does not automatically exclude the presence of quantum correlations [6]. This is in particular the reason why quantum computation models relying on mixed, separable (not entangled) states [7][8][9] are possible.The quantum discord [10, 11] is a measure of quantum correlations (see, however Refs. [11,12] for Holevo-type and thermodynamic based measures) which captures correlations beyond entanglement; it is defined as the difference of two classically equivalent formulas for mutual information and is non-negative. Due to the null volume of the set of zero-discord states [13], discord measures are not expected to undergo sudden death which is characteristic for entanglement evolutions [14][15][16]. The geometric measure of the discord describes the amount of correlations in a quantum system by finding the minimal Hilbert-Schmidt distance to the set of zero-discord states [17]. Recently, a lower [17] and an upper [18] bound on the geometric discord which can be calculated from a two-qubit density matrix have been found, which substantially simplifies the problem of studying the evolution of the quantum discord and opens the path for a qualitative and quantitative description of the decay of quantum correlations in realistic open quantum systems.In this paper we study the evolution of the lower and upper bounds of the geometric discord of two exciton quantum dot (QD) qubits interacting with an open phonon environment in order to capture the physical aspects of decoherence effects on quantum correlations. The interactions present in the system and the resulting dynamics are well understood. The experimentally observed evolution on picosecond timescales [19,20] can be described by pure dephasing within the independent boson model [20,21]. Super-Oh...

Phonon-mediated generation of quantum correlations between quantum dot qubits

“…In the presence of phonons these oscillations are damped while finite periods of time appear when entanglement is equal to zero 6 (sudden death type behaviour followed by the rebirth of entanglement). In the case of the quantum discord, the same oscillations are seen, but phonon dephasing leads to characteristic indifferentiable behavior near the state with highest entanglement, while discord curves are smooth around the zero-discord states 30 .…”

“…In the case of the quantum discord, the same oscillations are seen, but phonon dephasing leads to characteristic indifferentiable behavior near the state with highest entanglement, while discord curves are smooth around the zero-discord states. 30 It turns out that the described process can only lead to emergence of inter-qubit entanglement in extreme situations, for which the number of phonon modes taken into account is severely restricted and the exciton-phonon coupling is extremely high.…”

“…The long-time values of the X-state discord clearly show the transition between different regimes of decay (here as a function of α| 2 ) which is characteristic of the discord. 30,[34][35][36] The transition is occurs when the dependence of the discord as a function of |α| 2 changes between increasing and decreasing (on the left plots in Fig. 2).…”

A scheme for direct detection of qubit–environment entanglement generated during qubit pure dephasing

“…The scheme works only within the class of Hamiltonians that leads to qubit pure dephasing, but it involves operations and measurements performed only on the qubit. The required operations are well within reach of all systems that have been proposed as qubits, especially in the solid state, where pure dephasing is commonly the dominant source of decoherence [32][33][34][35][36][37][38][39][40]. The scheme relies on the fact that although it is the state of the environment which is distinctly affected by the presence of QEE, it can in turn influence the evolution of the qubit.…”

Topology of quantum discord

“…This will allow us to characterize in a topological fashion all joint evolutions of entanglement and discord that lead to the disappearance of both. Some evolutions have been computed by previous authors 22,23 .…”