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Register a new userMeasurement-device-independent quantification of irreducible high-dimensional entanglement
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The certification of entanglement dimensionality is of great importance in characterizing quantum systems. Recently, it is pointed out that quantum correlation of high-dimensional states can be simulated with a sequence of lower-dimensional states. Such problem may render existing characterization protocols unreliable---the observed entanglement may not be a truly high-dimensional one. Here, we introduce the notion of irreducible entanglement to capture its dimensionality that is indecomposable in terms of a sequence of lower-dimensional entangled systems. We prove this new feature can be detected in a measurement-device-independent manner with an entanglement witness protocol. To demonstrate the practicability of this technique, we experimentally apply it on a 3-dimensional bipartite state and the result certifies the existence of irreducible (at least) 3-dimensional entanglement.
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Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation of a Bell inequality. In this work, we provide the direct link between Bell nonlocality and the quantification of measurement incompatibility. This includes quantifiers for both incompatible and genuine-multipartite incompatible measurements. Our method straightforwardly generalizes to include constraints on the systems dimension (semi-device-independent approach) and on projective measurements, providing improved bounds on incompatibility quantifiers, and to include the prepare-and-measure scenario.
Using the concept of non-degenerate Bell inequality, we show that quantum entanglement, the critical resource for various quantum information processing tasks, can be quantified for any unknown quantum states in a semi-device-independent manner, where the quantification is based on the experimentally obtained probability distribution and beforehand knowledge on quantum dimension only. Specifically, as an application of our approach on multi-level systems, we experimentally quantify the entanglement of formation and the entanglement of distillation for qutrit-qutrit quantum systems. In addition, to demonstrate our approach for multi-partite systems, we further quantify the geometry measure of entanglement of three-qubit quantum systems. Our results supply a general way to reliably quantify entanglement in multi-level and multi-partite systems, thus paving the way to characterize many-body quantum systems by quantifying involved entanglement.
An important problem in quantum information processing is the certification of the dimension of quantum systems without making assumptions about the devices used to prepare and measure them, that is, in a device-independent manner. A crucial question is whether such certification is experimentally feasible for high-dimensional quantum systems. Here we experimentally witness in a device-independent manner the generation of six-dimensional quantum systems encoded in the orbital angular momentum of single photons and show that the same method can be scaled, at least, up to dimension 13.
The problem of demonstrating entanglement is central to quantum information processing applications. Resorting to standard entanglement witnesses requires one to perfectly trust the implementation of the measurements to be performed on the entangled state, which may be an unjustified assumption. Inspired by the recent work of F. Buscemi [Phys. Rev. Lett. 108, 200401 (2012)], we introduce the concept of Measurement-Device-Independent Entanglement Witnesses (MDI-EWs), which allow one to demonstrate entanglement of all entangled quantum states with untrusted measurement apparatuses. We show how to systematically obtain such MDI-EWs from standard entanglement witnesses. Our construction leads to MDI-EWs that are loss-tolerant, and can be implemented with current technology.
Experimental detection of entanglement of an arbitrary state of a given bipartite system is crucial for exploring many areas of quantum information. But such a detection should be made in a device independent way if the preparation process of the state is considered to be faithful, in order to avoid detection of a separable state as entangled one. The recently developed scheme of detecting bipartite entanglement in a measurement device independent way [Phys. Rev. Lett {bf 110}, 060405 (2013)] does require information about the state. Here by using Auguisiak et al.s universal entanglement witness scheme for two-qubit states [Phys. Rev. A {bf 77}, 030301 (2008)], we provide a universal detection scheme for two-qubit states in a measurement device independent way. We provide a set of universal witness operators for detecting NPT-ness(negative under partial transpose) of states in a measurement device independent way. We conjecture that no such universal entanglement witness exists for PPT(positive under partial transpose) entangled states. We also analyse the robustness of some of the experimental schemes of detecting entanglement in a measurement device independent way under the influence of noise in the inputs (from the referee) as well as in the measurement operator as envisazed in ref. [Phys. Rev. Lett {bf 110}, 060405 (2013)].
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