Role of Quantumness of Correlations in Entanglement Resource Theory

Quantum correlations: entanglement and quantumness of correlations are main resource for quantum information theory. In this chapter it is presented the scenarios which quantumness of correlations plays an interesting role in entanglement distillation protocol. By means of Koashi - Winter relation, it is discussed that quantumness of correlations are related to the irreversibility of the entanglement distillation protocol. The activation protocol is introduced, and it is proved that quantumness of correlations can create distillable entanglement between the system and the measurement apparatus during a local measurement process.Comment: Full chapter contribution of Advanced Technologies of Quantum Key Distribution, ISBN 978-953-51-5289-

Maintaining the Adversarial System: The Practice of Allowing Jurors to Question Witnesses During Trial

A defendant sits in the witness stand undergoing examination by his attorney. He is accused of armed robbery, among other criminal acts. During the course of the defendant\u27s testimony, a juror blurts out that he has a question. The judge tells the juror to write his question down and advises the juror that he will be able to ask his question upon completion of the attorneys\u27 examinations. When the juror\u27s question is finally asked, the judge indicates to the defendant\u27s attorney that the attorney should address the matter raised by the juror on reexamination. During the reexamination, the attorney turns to the jury box and directly addresses the individual juror, inquiring whether the juror\u27s question had been sufficiently answered. At this point, several other jurors, feeling released from their silence, also begin questioning the witness. The judge or attorneys occasionally rephrase the questions, but often the witness answers the jurors directly. Neither party objects to the jurors\u27questions at the time of trial. The members of the jury in the trial discussed above appear to have acted as inquisitors. Instead of listening passively to the presentation of evidence from the opposing parties, they pose their own questions to the defendant. In an inquisitorial system of justice, used in many civil law countries, judges or juries have the primary responsibility for gathering and evaluating evidence. These fact finders actively seek evidence, such that the parties become mere objects of inquiry rather than the directors of the trial. In contrast to the inquisitorial system, the United States\u27 adversarial system assigns the primary responsibility for the development and presentation of evidence to the parties themselves. In the adversarial system, an impartial fact finder decides a case based on the conflicting evidence presented by opposing parties. The depiction above, however, describes not a trial governed by the inquisitorial system of justice, but rather a recent trial in the Eastern District of New York. Commentators and courts are currently questioning the efficacy of our jury system. Some view the system as too rigid and unreliable a truth-finding body. These critics suggest altering aspects of the jury system, and most recommend alterations that encourage a more active and involved jury. One such proposed alteration would permit the jury to pose questions to witnesses during trial. Many jurisdictions are either considering or are currently experimenting with the use of juror questioning

Witnessed entanglement and the geometric measure of quantum discord

We establish relations between geometric quantum discord and entanglement quantifiers obtained by means of optimal witness operators. In particular, we prove a relation between negativity and geometric discord in the Hilbert-Schmidt norm, which is slightly different from a previous conjectured one [Phys. Rev. A 84, 052110 (2011)].We also show that, redefining the geometric discord with the trace norm, better bounds can be obtained. We illustrate our results numerically.Comment: 8 pages + 3 figures. Revised version with erratum for PRA 86, 024302 (2012). Simplified proof that discord is bounded by entanglement in any nor

Quantum Correlations and Coherence in Spin-1 Heisenberg Chains

We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that as none of the studied measures can detect the infinite order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point.Comment: 8 pages. 5 figure