Optimal classical-communication-assisted local model of n-qubit Greenberger-Horne-Zeilinger correlations

We present a model, motivated by the criterion of reality put forward by Einstein, Podolsky, and Rosen and supplemented by classical communication, which correctly reproduces the quantum-mechanical predictions for measurements of all products of Pauli operators on an n-qubit GHZ state (or ``cat state''). The n-2 bits employed by our model are shown to be optimal for the allowed set of measurements, demonstrating that the required communication overhead scales linearly with n. We formulate a connection between the generation of the local values utilized by our model and the stabilizer formalism, which leads us to conjecture that a generalization of this method will shed light on the content of the Gottesman-Knill theorem.Comment: New version - expanded and revised to address referee comment

COMPLEMENTARITY RELATIONS FOR MULTI-QUBIT SYSTEMS

We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the degree to which single particle properties are possessed by an individual member of the system is limited by the bipartite entanglement that exists between that qubit and the remainder of the system. This result implies that the phenomenon of entanglement sharing is one specific consequence of complementarity. The second expression, which holds for an arbitrary state of two qubits, pure or mixed, quantifies a tradeoff between the amounts of entanglement, separable uncertainty, and single particle properties that are encoded in the quantum state. The separable uncertainty is a natural measure of our ignorance about the properties possessed by individual subsystems, and may be used to completely characterize the relationship between entanglement and mixedness in two-qubit systems. The two-qubit complementarity relation yields a useful geometric picture in which the root mean square values of local subsystem properties act like coordinates in the space of density matrices, and suggests possible insights into the problem of interpreting quantum mechanics

Entanglement Sharing in the Tavis-Cummings Model

Individual members of an ensemble of identical systems coupled to a common probe can become entangled with one another, even when they do not interact directly. We investigate how this type of multipartite entanglement is generated in the context of a system consisting of an ensemble of N two-level atoms resonantly coupled to a single mode of the electromagnetic field. In the case where N = 2, the dynamical evolution is studied in terms of the entanglements in the different bipartite divisions of the system, as quantified by the I-tangle. We also propose a generalization of the so-called residual tangle that quantifies the inherent three-body correlations in this tripartite system. This allows us to give a complete characterization of the phenomenon of entanglement sharing in the case of the two-atom Tavis-Cummings model. We also introduce an entanglement monotone which constitutes a lower bound on the I-tangle of an arbitrary bipartite system. This measure is seen to be useful in quantifying the entanglement in various bipartite partitions of the TCM in the case where N> 2, i.e., when there is no known analytic form for the I-tangle. Keywords: Entanglement, Entanglement-Sharing, Tavis-Cummings Model 1