Measurements of Nonlocal Variables and Demonstration of the Failure of the Product Rule for a Pre- and Postselected Pair of Photons.

We report the first implementation of the von Neumann instantaneous measurements of nonlocal variables, which becomes possible due to technological achievements in creating hyperentangled photons. Tests of reliability and of the nondemolition property of the measurements have been performed with high precision, showing the suitability of the scheme as a basic ingredient of numerous quantum information protocols. The method allows us to demonstrate for the first time with strong measurements a special feature of pre- and postselected quantum systems: the failure of the product rule. It has been verified experimentally that for a particular pre- and postselected pair of particles, a single measurement on particle A yields with certainty σ_{x}^{A}=-1, a single measurement on particle B yields with certainty σ_{y}^{B}=-1, and a single nonlocal measurement on particles A and B yields with certainty σ_{x}^{A}σ_{y}^{B}=-1.

Universality of local weak interactions and its application for interferometric alignment.

The modification of the effect of interactions of a particle as a function of its preselected and postselected states is analyzed theoretically and experimentally. The universality property of this modification in the case of local interactions of a spatially preselected and postselected particle has been found. It allowed us to define an operational approach for the characterization of the presence of a quantum particle in a particular place: the way it modifies the effect of local interactions. The experiment demonstrating this universality property provides an efficient interferometric alignment method, in which the position of the beam on a single detector throughout one phase scan yields all misalignment parameters.

Publisher's Note: Multipartite Entanglement Detection with Minimal Effort [Phys. Rev. Lett. 117, 210504 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.117.210504.

Multipartite Entanglement Detection with Minimal Effort.

Certifying entanglement of a multipartite state is generally considered a demanding task. Since an N qubit state is parametrized by 4^{N}-1 real numbers, one might naively expect that the measurement effort of generic entanglement detection also scales exponentially with N. Here, we introduce a general scheme to construct efficient witnesses requiring a constant number of measurements independent of the number of qubits for states like, e.g., Greenberger-Horne-Zeilinger states, cluster states, and Dicke states. For four qubits, we apply this novel method to experimental realizations of the aforementioned states and prove genuine four-partite entanglement with two measurement settings only.

Genuine Multipartite Entanglement without Multipartite Correlations.

Nonclassical correlations between measurement results make entanglement the essence of quantum physics and the main resource for quantum information applications. Surprisingly, there are n-particle states which do not exhibit n-partite correlations at all but still are genuinely n-partite entangled. We introduce a general construction principle for such states, implement them in a multiphoton experiment and analyze their properties in detail. Remarkably, even without multipartite correlations, these states do violate Bell inequalities showing that there is no classical, i.e., local realistic model describing their properties.

Systematic errors in current quantum state tomography tools.

Common tools for obtaining physical density matrices in experimental quantum state tomography are shown here to cause systematic errors. For example, using maximum likelihood or least squares optimization to obtain physical estimates for the quantum state, we observe a systematic underestimation of the fidelity and an overestimation of entanglement. Such strongly biased estimates can be avoided using linear evaluation of the data or by linearizing measurement operators yielding reliable and computational simple error bounds.