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      Witnessing entanglement without entanglement witness operators

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          Abstract

          <p id="d15880871e218">The experimental detection and theoretical characterization of entanglement in many-body systems is a mostly unsolved problem. Here we relate entanglement to the statistical speed measuring how quickly nearby states become distinguishable under the action of an arbitrary many-body Hamiltonian. The method is remarkably simple: We witness multipartite entanglement, just elaborating on published experimental data with ions and photons. The unveiled connection between the statistical speed and entanglement provides a unifying framework that can shed new light on quantum information science and quantum critical phenomena. </p><p class="first" id="d15880871e221">Quantum mechanics predicts the existence of correlations between composite systems that, although puzzling to our physical intuition, enable technologies not accessible in a classical world. Notwithstanding, there is still no efficient general method to theoretically quantify and experimentally detect entanglement of many qubits. Here we propose to detect entanglement by measuring the statistical response of a quantum system to an arbitrary nonlocal parametric evolution. We witness entanglement without relying on the tomographic reconstruction of the quantum state, or the realization of witness operators. The protocol requires two collective settings for any number of parties and is robust against noise and decoherence occurring after the implementation of the parametric transformation. To illustrate its user friendliness we demonstrate multipartite entanglement in different experiments with ions and photons by analyzing published data on fidelity visibilities and variances of collective observables. </p>

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          Is Open Access

          Quantum entanglement

          All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory}. But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized.
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            Statistical distance and the geometry of quantum states

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              Separability of Mixed States: Necessary and Sufficient Conditions

              We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for \(2\times2\) and \(2\times3\) systems. Here, the positivity of the partial transposition of a state is necessary and sufficient for its separability. However, it is not the case in general. Some examples of mixtures which demonstrate the utility of the criterion are considered.
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                Author and article information

                Journal
                Proceedings of the National Academy of Sciences
                Proc Natl Acad Sci USA
                Proceedings of the National Academy of Sciences
                0027-8424
                1091-6490
                October 11 2016
                October 11 2016
                : 113
                : 41
                : 11459-11464
                Article
                10.1073/pnas.1603346113
                5068306
                27681625
                c3cdd7d5-491a-4265-ae44-6ac615648968
                © 2016

                http://www.pnas.org/site/misc/userlicense.xhtml

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