Collapse of the quantum correlation hierarchy links entropic uncertainty to entanglement creation

Quantum correlations have fundamental and technological interest, and hence many measures have been introduced to quantify them. Some hierarchical orderings of these measures have been established, e.g., discord is bigger than entanglement, and we present a class of bipartite states, called premeasurement states, for which several of these hierarchies collapse to a single value. Because premeasurement states are the kind of states produced when a system interacts with a measurement device, the hierarchy collapse implies that the uncertainty of an observable is quantitatively connected to the quantum correlations (entanglement, discord, etc.) produced when that observable is measured. This fascinating connection between uncertainty and quantum correlations leads to a reinterpretation of entropic formulations of the uncertainty principle, so-called entropic uncertainty relations, including ones that allow for quantum memory. These relations can be thought of as lower-bounds on the entanglement created when incompatible observables are measured. Hence, we find that entanglement creation exhibits complementarity, a concept that should encourage exploration into "entanglement complementarity relations".Comment: 19 pages, 2 figures. Added Figure 1 and various remarks to improve clarity of presentatio

Optimal estimation of entanglement

Entanglement does not correspond to any observable and its evaluation always corresponds to an estimation procedure where the amount of entanglement is inferred from the measurements of one or more proper observables. Here we address optimal estimation of entanglement in the framework of local quantum estimation theory and derive the optimal observable in terms of the symmetric logarithmic derivative. We evaluate the quantum Fisher information and, in turn, the ultimate bound to precision for several families of bipartite states, either for qubits or continuous variable systems, and for different measures of entanglement. We found that for discrete variables, entanglement may be efficiently estimated when it is large, whereas the estimation of weakly entangled states is an inherently inefficient procedure. For continuous variable Gaussian systems the effectiveness of entanglement estimation strongly depends on the chosen entanglement measure. Our analysis makes an important point of principle and may be relevant in the design of quantum information protocols based on the entanglement content of quantum states.Comment: 9 pages, 2 figures, v2: minor correction

Operational one-to-one mapping between coherence and entanglement measures

We establish a general operational one-to-one mapping between coherence measures and entanglement measures: Any entanglement measure of bipartite pure states is the minimum of a suitable coherence measure over product bases. Any coherence measure of pure states, with extension to mixed states by convex roof, is the maximum entanglement generated by incoherent operations acting on the system and an incoherent ancilla. Remarkably, the generalized CNOT gate is the universal optimal incoherent operation. In this way, all convex-roof coherence measures, including the coherence of formation, are endowed with (additional) operational interpretations. By virtue of this connection, many results on entanglement can be translated to the coherence setting, and vice versa. As applications, we provide tight observable lower bounds for generalized entanglement concurrence and coherence concurrence, which enable experimentalists to quantify entanglement and coherence of the maximal dimension in real experiments.Comment: 14 pages, 1 figure, new results added, published in PR

Lower bounds on entanglement measures from incomplete information

How can we quantify the entanglement in a quantum state, if only the expectation value of a single observable is given? This question is of great interest for the analysis of entanglement in experiments, since in many multiparticle experiments the state is not completely known. We present several results concerning this problem by considering the estimation of entanglement measures via Legendre transforms. First, we present a simple algorithm for the estimation of the concurrence and extensions thereof. Second, we derive an analytical approach to estimate the geometric measure of entanglement, if the diagonal elements of the quantum state in a certain basis are known. Finally, we compare our bounds with exact values and other estimation methods for entanglement measures.Comment: 9 pages, 4 figures, v2: final versio

Cosmological dark energy effects from entanglement

The thorny issue of relating information theory to cosmology is here addressed by assuming a possible connection between quantum entanglement measures and observable universe. In particular, we propose a cosmological toy model, where the equation of state of the cosmological fluid, which drives the today observed cosmic acceleration, can be inferred from quantum entanglement between different cosmological epochs. In such a way the dynamical dark energy results as byproduct of quantum entanglement.Comment: 5 pages, to be published in Phys. Lett.

Direct measurement of finite-time disentanglement induced by a reservoir

We propose a method for directly probing the dynamics of disentanglement of an initial two-qubit entangled state, under the action of a reservoir. We show that it is possible to detect disentanglement, for experimentally realizable examples of decaying systems, through the measurement of a single observable, which is invariant throughout the decay. The systems under consideration may lead to either finite-time or asymptotic disentanglement. A general prescription for measuring this observable, which yields an operational meaning to entanglement measures, is proposed, and exemplified for cavity quantum electrodynamics and trapped ions.Comment: 4 pages, 2 figure