A simple analytical expression of quantum Fisher and Skew information and their dynamics under decoherence channels

In statistical estimation theory, it has been shown previously that the Wigner-Yanase skew information is bounded by the quantum Fisher information associated with the phase parameter. Besides, the quantum Cram\'er-Rao inequality is expressed in terms of skew information. Since these two fundamental quantities are based on the concept of quantum uncertainty, we derive here their analytical formulas for arbitrary two-qubit $X$-states using the same analytical procedures. A comparison of these two informational quantifiers for two quasi-Werner states composed of two bipartite superposed coherent states is examined. Moreover, we investigated the decoherence effects on such quantities generated by the phase damping, depolarization and amplitude damping channels. We showed that decoherence strongly influences the initial quantum criteria and these quantities exhibit similar dynamic behaviors. This current work is characterized by the fact that these two concepts play the same role and capture similar properties in quantum estimation protocols

Quantum states with a positive partial transpose are useful for metrology

We show that multipartite quantum states that have a positive partial transpose with respect to all bipartitions of the particles can outperform separable states in linear interferometers. We introduce a powerful iterative method to find such states. We present some examples for multipartite states and examine the scaling of the precision with the particle number. Some bipartite examples are also shown that possess an entanglement very robust to noise. We also discuss the relation of metrological usefulness to Bell inequality violation. We find that quantum states that do not violate any Bell inequality can outperform separable states metrologically. We present such states with a positive partial transpose, as well as with a non-positive positive partial transpose.Comment: 6 pages including two figures + three-page supplement including two figures using revtex 4.1, with numerically obtained density matrices as text files; v2: published version; v3: published version, typo in the 4x4 bound entangled state is corrected (noticed by Peng Yin

Enhanced quantum channel uncertainty relations by skew information

By revisiting the mathematical foundation of the uncertainty relation, skew information-based uncertainty sequences are developed for any two quantum channels. A reinforced version of the Cauchy-Schwarz inequality is adopted to improve the uncertainty relation, and a sampling technique of observables' coordinates is used to offset randomness in the inequality. It is shown that the lower bounds of the uncertainty relations are tighter than some previous studies

Entanglement and its operational measure

An operational representation of concurrence measuring the entanglement of bipartite systems by means of averages of basic observables is discussed. We prove the validity of this representation for bipartite systems with any dimension of a single-party Hilbert space. We show that Wigner-Yanase "skew" information gives a reasonable estimation of the amount of entanglement (in ebits) carried by mixed two-qubit states. ©2006 Springer Science+Business Media, Inc