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arXiv:1101.4983

Nullity of quantum discord of two-qubit X-state systems

Gao‐xiang Li, Zhen Yi, Z. Ficek

Published Jan 26, 2011• 5 citations
arXivHTMLPDF

Abstract

The conditions are established for nullity of quantum discord for mixed states of a general two-qubit system whose dynamical behaviour is given by an X-state form density matrix. It is found that quantum discord can vanish at a finite time even in the presence of correlations between qubits. The degeneracy of the populations of the combined states of the qubits and the multi-qubit quantum coherences are shown to be responsible for vanishing of the discord. We illustrate our considerations by examining the coherent-state Tavis-Cummings model in which two qubits interact dispersively with the cavity field. The disappearance of the discord is shown to be dependent on the initial atomic conditions that it may occur at a discrete instance or periodically at discrete instances redistributed over whole range of the evolution time. The nullity of the discord is interpreted as resulting from equal preparation of the spin anti-correlated and spin correlated product states in superposition~states.

DOI
10.48550/arxiv.1101.4983

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The conditions are established for nullity of quantum discord for mixed states of a general two-qubit system whose dynamical behaviour is given by an X-state form density matrix. It is found that quantum discord can vanish at a finite time even in the presence of correlations between qubits. The degeneracy of the populations of the combined states of the qubits and the multi-qubit quantum coherences are shown to be responsible for vanishing of the discord. We illustrate our considerations by examining the coherent-state Tavis-Cummings model in which two qubits interact dispersively with the cavity field. The disappearance of the discord is shown to be dependent on the initial atomic conditions that it may occur at a discrete instance or periodically at discrete instances redistributed over whole range of the evolution time. The nullity of the discord is interpreted as resulting from equal preparation of the spin anti-correlated and spin correlated product states in superposition~states.
The dynamics of quantum discord for two identical qubits in two independent single-mode cavities and a common single-mode cavity are discussed. For the initial Bell state with correlated spins, while the entanglement sudden death can occur, the quantum discord vanishes only at discrete moments in the independent cavities and never vanishes in the common cavity. Interestingly, quantum discord and entanglement show opposite behavior in the common cavity, unlike in the independent cavities. For the initial Bell state with anti-correlated spins, quantum discord and entanglement behave in the same way for both independent cavities and a common cavity. It is found that the detunings always stabilize the quantum discord.
Abstract We revisit the problem of the dynamics of quantum correlations in the Tavis–Cummings model. Our results show that the dynamics of entanglement and quantum discord are far from being trivial or intuitive. We find states with the same entanglement but different discord and states where the two quantifiers give opposite information about correlations at a certain time. We furthermore show that many of the dynamical features of quantum discord attributed to dissipation are already present in the exact framework and are due to the characteristic quantum nonlinearity of the model and to the choice of initial conditions. Through a comprehensive analysis of pure and mixed initial conditions, we find a fascinating range of phenomena that can be used for experimental purposes. We propose an experiment called quantum discord gates where for a given pure initial condition discord is zero or non-zero depending on the number of photons in the cavity. Given the marginal character of states with zero discord this result is not only completely counterintuitive but is also useful as a way to count photons.
We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We, first, introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state with maximum discord. The experimental and simulated behavior of rise and fall of discord agree fairly well. (b) We examine the efficiency of dynamical decoupling sequences in preserving quantum correlations. In our experimental setup, the dynamical decoupling sequences preserved the traceless parts of the density matrices at high fidelity. But they could not maintain the purity of the quantum states and so were unable to keep the discord from decaying. (c) We observe the evolution of discord for a singlet-triplet mixed state during a radio-frequency spin-lock. A simple relaxation model describes the evolution of discord, and the accompanying evolution of fidelity of the long-lived singlet state, reasonably well.
We study the dynamics of classical correlation and quantum discord of two coupled two-level atoms interacting with a cavity initially in vacuum, coherent and thermal equilibrium states, respectively. The interplay between the atom–atom coupling and mean number of photons is considered. We find that, for a cavity in a vacuum state, classical correlation or quantum discord shows a sudden change in behaviour during the evolution, and evolves periodically for zero and very large qubit–qubit couplings. However, for coherent and thermal equilibrium states, the classical correlation and quantum discord present the phenomenon of collapse–revival when the qubit–qubit coupling is much greater than the mean number of photons. The period of collapse–revival becomes long as the qubit–qubit coupling and mean number of photons increase. The relationship between quantum discord and entanglement in the studied system is considered.
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.
We investigate the dynamic behaviors of quantum discord for a central two-qubit system coupled to an XY\mathit{XY}XY-spin-chain environment. In the weak-coupling regime, we show that the quantum discord for the two central qubits can become minimized rapidly close to the critical point of a quantum phase transition. By considering the two qubits that are initially prepared in the Werner state, we study the evolution of the quantum discord and that of entanglement under the same conditions. Our results imply that entanglement can disappear completely after a finite time, while the quantum discord decreases and tends to be a stable value according to the initial-state parameter for a very-long-time interval. In this sense, the quantum discord is more robust than entanglement for the quantum system exposed to the environment. The relation between the quantum correlations and the classical correlation is also shown for two particular cases.