Sudden decoherence transitions for quantum discord

Abstract

We investigate the disappearance of discord in 2-and multi-qubit systems subject to decohering influences. We formulate the computation of quantum discord and quantum geometric discord in terms of the generalized Bloch vector, which gives useful insights on the time evolution of quantum coherence for the open system, particularly the comparison of entanglement and discord. We show that the analytical calculation of the global geometric discord is NP-hard in the number of qubits, but a similar statement for global entropic discord is more difficult to prove. We present an efficient numerical method to calculating the quantum discord for a certain important class of multipartite states. In agreement with previous work for 2-qubit cases, (Mazzola et al., Phys. Rev. Lett. 104, 200401 (2010)), we find situations in which there is a sudden transition from classical to quantum decoherence characterized by the discord remaining relatively robust (classical decoherence) until a certain point from where it begins to decay quickly whereas the classical correlation decays more slowly (quantum decoherence). However, we find that as the number of qubits increases, the chance of this kind of transition occurring becomes small.

Topology of quantum discord

“…'Frozen' quantum discord occurs when D t ( ) or D t G ( ) is constant positive number for a finite interval of time. During this time period, the quantum mutual information and the classical correlations decrease, but the difference = − D I J class remains fixed [15,31]. Since surfaces of zero discord can have simple shapes in N-space [25], surfaces of constant geometric discord can also have relatively simple shapes and simple plausible models can produce the phenomenon of frozen discord.…”

“…The time evolution is given by equation (28). For (c) and (d) the initial state is a Bell-diagonal state that evolves according to equation (31) with entanglement parameter β = 1 2 / (c) and β = 1 4 / (d). The entanglement of formation is an increasing function of the concurrence, which accounts for the similarity in the results.…”

Phonon-mediated generation of quantum correlations between quantum dot qubits

“…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).…”

Condition for zero and nonzero discord in graph Laplacian quantum states

“…Recall that quantum discord D(ρ) of a state ρ is a class of quantum correlations which has been used as a resource in quantum information and communication [12,13,14,15,16,17]. From the perspective of computational complexity, it is proved that calculating D(ρ) is an NP-complete problem [18,19]. This calls for developing alternate measures and techniques to realize quantum discord [20].…”