Environment-Induced Sudden Transition in Quantum Discord Dynamics

Nonclassical correlations play a crucial role in the development of quantum information science. The recent discovery that nonclassical correlations can be present even in separable (nonentangled) states has broadened this scenario. This generalized quantum correlation has been increasing in relevance in several fields, among them quantum communication, quantum computation, quantum phase transitions, and biological systems. We demonstrate here the occurrence of the sudden-change phenomenon and immunity against some sources of noise for the quantum discord and its classical counterpart, in a room temperature nuclear magnetic resonance setup. The experiment is performed in a decohering environment causing loss of phase relations among the energy eigenstates and exchange of energy between system and environment, resulting in relaxation to the Gibbs ensemble.

Figure 1

Sketch of the pulse sequence used experimentally to follow the dynamics of quantum and classical correlations under decoherence. The sequence consists of three blocks: the initial state preparation, relaxation delay, and readout by quantum state tomography.

Figure 2

Sudden change in behavior of correlations. (a) Bar representation of the real and, (b) imaginary parts of the initial deviation matrix for the sudden-change experiment, reconstructed by quantum state tomography. We adopted the usual computational basis, where $|0⟩$ and $|1⟩$ represent the eigenstates of ${\sigma }_z$ for each qubit. (c) displays the predicted sudden change in behavior of the correlations during their dynamic evolution to thermal equilibrium. The blue circles are the experimental data for the quantum mutual information, while the red squares and green triangles represent the classical and quantum correlations, respectively. The black lines are the theoretical predictions. The initial state is analogous to the state in Eq. (2) with $|c_x|$, $|c_y|>|c_z|$. The correlations are displayed in units of $({\epsilon }^2/\ln 2)\mathrm{bit}$.

Figure 3

Immunity against decoherence. (a) Bar representation of the real and, (b) imaginary parts of the initial deviation matrix, reconstructed by quantum state tomography. (c) shows that the classical correlation is not affected by the action of the phase-damping channel. The small decay rate is entirely due to the amplitude-damping channel. The displayed pattern is the same as in Fig. 2. For this experiment, the initial state is analogous to the state in Eq. (2) with $|c_z|>|c_x|$, $|c_y|$. The correlations are computed in units of $({\epsilon }^2/\ln 2)\mathrm{bit}$.