We investigate the geometric measure of quantum discord of all possible bipartite divisions of a tripartite system of Dirac fields in noninertial frames. As a comparison, we calculate the geometric measure of entanglement. We discuss the properties of geometric measure of quantum discord and geometric measure of entanglement for three qubit–qubit subsystems with acceleration parameter and the parameter describing the degree of entanglement the system in detail. We have found a conservative relationship involving two of three geometric discords in some condition and another conservative relationship involving three geometric discords for initially maximally entangled states. By the way, we also report some conservative relationships of concurrence, mutual information and geometric measure of entanglement for two bipartite subsystems.
We investigate the geometric measure of quantum discord of all possible bipartite divisions of a tripartite system of Dirac fields in noninertial frames. As a comparison, we calculate the geometric measure of entanglement. We discuss the properties of geometric measure of quantum discord and geometric measure of entanglement for three qubit–qubit subsystems with acceleration parameter and the parameter describing the degree of entanglement the system in detail. We have found a conservative relationship involving two of three geometric discords in some condition and another conservative relationship involving three geometric discords for initially maximally entangled states. By the way, we also report some conservative relationships of concurrence, mutual information and geometric measure of entanglement for two bipartite subsystems.
Abstract Using the single-mode approximation we study the quantum correlations of a free Dirac field on the Werner state in the noninertial frame. We present analytical quantum discord D and its geometric measurement D G . We notice that the quantum discord still exists for the system ρ ARI even in the acceleration limit. We also calculate the entanglement of formation (EOF) and the geometric measure of entanglement ( E G ) to compare the behaviors of the entanglement with the quantum discord. The entanglement is nonzero for the fidelity of the Werner state with a Bell state F > 0.5, while the quantum discord is equal to zero only for F = 0.25. We also observe that the quantum discord is more robust to the change of acceleration than the entanglement, which is more sensitive to the acceleration.
We study the quantification of geometric discord for tripartite quantum systems. Firstly, we obtain the analytic formula of geometric discord for tripartite pure states. It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems, the results presented here show that this property is no longer true in tripartite systems. Furthermore, we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination, that is, we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement. Lastly, we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence. It is interesting that the frozen phenomenon exists for geometric discord in this scenario.
We revisit the ``field entanglement in noninertial frames'' scenario extensively studied in previous literature and demonstrate that the geometric discord, a proposed measure of generalized quantum correlations, decays to zero in the infinite acceleration limit. This is in contrast with previous research showing that the acceleration-induced degradation of quantum discord was not strong enough to extinguish discord in this limit. We argue that our finding has two opposing but noncontradicting implications. On the one hand, the usable quantum correlations in the large acceleration regime appear severely limited for any protocols making use of geometric discord as a figure of merit. On the other hand, our result indicates, in corroboration with other recent work, that the geometric discord is not a faithful measure of quantum correlations, especially in the case of continuous-variable systems, due to the existence of states which have finite quantum discord but are nevertheless infinitesimally close (in the Hilbert-Schmidt norm) to a zero-discord state.
Quantum entanglement plays a key role in quantum information and quantum computation and thus attracts much attention in many branches of physics both in theory and in experiment. But recent studies revealed that some separable states (non-entangled state) may speed up certain tasks over their classical counterparts and may also possess certain kinds of quantum correlations. For example, geometric quantum discord, which is a more general quantum correlation measure than entanglement, can be nonzero for some separable states. From a practical point of view, it is proposed that the geometric quantum discord be responsible for the power of many quantum information processing tasks. In order to capture such correlations, Ollivier and Zurek introduced quantum discord, which measures the discrepancy between two natural yet different quantum analogues of two classically equivalent expressions of mutual information. However, the calculation of quantum discord is based on numerical maximization procedure, and there are few analytical expressions even for a two-qubit state. In order to obtain the analytical results of quantum discord, a geometric measure of quantum discord which measures the quantum correlations through the minimum Hilbert-Schmidt distance between the given state and zero discord state is introduced. Geometric quantum discord is defined as an effective measure of quantum correlation, and the geometric quantum discord through the minimal distance between the quantum state and the set of zero-discord states in a bipartite quantum system can be worked out. In this paper, by using the geometric quantum discord measurement method, the geometric quantum discord in Tavis-Cummings model is investigated, and the influences of the initial state purity, entanglement degree, dipole-dipole coupling intensity between two atoms, and field in the Fock state on the evolution characteristic of geometric quantum discord are analyzed. The results show that the geometric quantum discord appears periodically. It initially decreases to a minimum value, and then turns out to be increased for different initial states. The rigorous analysis and numerical results reveal that when we take a suitable initial state, the geometric quantum discord of two atoms can be kept in correlation. When the atoms are in the different initial states, the quantum properties of the system are significant. The photon number of the field can lead the quantum discord to be weakened. Geometric quantum discord can be increased by increasing the cavity photon number and the dipole-dipole coupling intensity. Geometric quantum discord can be enhanced obviously by increasing the strength of the dipole-dipole coupling interaction. The conclusions may conduce to the understanding of quantum correlation for the other systems from the view of geometric quantum discord.
We define a new measure of quantum correlations in bipartite quantum systems given by the Bures distance of the system state to the set of classical states with respect to one subsystem, that is, to the states with zero quantum discord. Our measure is a geometrical version of the quantum discord. As the latter it quantifies the degree of non-classicality in the system. For pure states it is identical to the geometric measure of entanglement. We show that for mixed states it coincides with the optimal success probability of an ambiguous quantum state discrimination task. Moreover, the closest zero-discord states to a state ρ are obtained in terms of the corresponding optimal measurements.
Abstract We investigate and compare three distinguished geometric measures of bipartite quantum correlations that have been recently introduced in the literature: the geometric discord, the measurement-induced geometric discord, and the discord of response, each one defined according to three contractive distances on the set of quantum states, namely the trace, Bures, and Hellinger distances. We establish a set of exact algebraic relations and inequalities between the different measures. In particular, we show that the geometric discord and the discord of response based on the Hellinger distance are easy to compute analytically for all quantum states whenever the reference subsystem is a qubit. These two measures thus provide the first instance of discords that are simultaneously fully computable, reliable (since they satisfy all the basic Axioms that must be obeyed by a proper measure of quantum correlations), and operationally viable (in terms of state distinguishability). We apply the general mathematical structure to determine the closest classical-quantum state of a given state and the maximally quantum-correlated states at fixed global state purity according to the different distances, as well as a necessary condition for a channel to be quantumness breaking.