It is argued that a weak value of an observable is a robust property of a single pre-and postselected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affects other systems as if it were in an eigenstate with eigenvalue equal to the weak value. This differs significantly from the action of a system pre-selected only and possessing a numerically equal expectation value. The weak value has a physical meaning beyond a conditional average of a pointer in the weak measurement procedure. The difference between the weak value and the expectation value has been demonstrated on the example of photon polarization. In addition, the weak values for systems pre-and post-selected in mixed states are considered.

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.

Quantum entanglement is usually revealed via a well aligned, carefully chosen set of measurements. Yet, under a number of experimental conditions, for example in communication within multiparty quantum networks, noise along the channels or fluctuating orientations of reference frames may ruin the quality of the distributed states. Here, we show that even for strong fluctuations one can still gain detailed information about the state and its entanglement using random measurements. Correlations between all or subsets of the measurement outcomes and especially their distributions provide information about the entanglement structure of a state. We analytically derive an entanglement criterion for two-qubit states and provide strong numerical evidence for witnessing genuine multipartite entanglement of three and four qubits. Our methods take the purity of the states into account and are based on only the second moments of measured correlations. Extended features of this theory are demonstrated experimentally with four photonic qubits. As long as the rate of entanglement generation is sufficiently high compared to the speed of the fluctuations, this method overcomes any type and strength of localized unitary noise.

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 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 A x = −1, a single measurement on particle B yields with certainty σ B y = −1, and a single nonlocal measurement on particles A and B yields with certainty σ A x σ B y = −1.All known interactions in nature are local. It was thus believed (e.g. [1]) that measurements of nonlocal variables (variables which are related to more than one region of space) are impossible. However, Aharonov and his coauthors [2, 3] showed theoretically that some nonlocal variables can be measured. For two separate locations the sum of local variables, A + B, and the modular sum, (A + B) mod c are always measurable. On the other hand, they also showed that some other nonlocal variables cannot be measured as this would lead to superluminal signalling. Note that if we do not require the measurement to be nondemolition, then theoretically all nonlocal variables are measurable [4], but the procedure has high demands on entanglement resources [5][6][7].Aharonov's main motivation was to shed light on relativistic quantum field theory [2,[8][9][10][11], but the main impact of the analysis of measurements of nonlocal variables was in the field of quantum information [12][13][14][15][16][17][18][19][20]. In particular, it allowed an efficient method for teleportation [21] and was the basis for cryptographic protocols [22][23][24][25].In this work we demonstrate the measurement of nonlocal variables in its original sense, the one which is closest to the standard von Neumann definition of measurement in quantum mechanics [26]. Note, that there exists an alternative scheme [27] alongside a particular proposal for its implementation [28,29], which, however, has the drawback of being a probabilistic measurement, i.e., even with ideal devices it might not provide an outcome.After performing and testing our measurement procedure we apply it to show the peculiar phenomenon of the failure of the product rule for two separate (and thus commuting) local variables which can take place only for pre-and postselected quantum systems [30][31][32]. There have been several demonstrations of the failure of the product rule for weak values, the outcomes of weak measurements [33][34][35] in the context of the Hardy paradox [30]. These, however, are very different results, obtained from many measurements on an ensemble of particles. In our scen...

We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32, 050303 (2015)] to the experiment of Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)

Is it possible that a measurement of a spin component of a spin-1/2 particle yields the value 100? In 1988 Aharonov, Albert and Vaidman argued that upon pre- and postselection of particular spin states, weakening the coupling of a standard measurement procedure ensures this paradoxical result1. This theoretical prediction, called weak value, was realised in numerous experiments2–9, but its meaning remains very controversial10–19, since its “anomalous” nature, i.e., the possibility to exceed the eigenvalue spectrum, as well as its “quantumness” are debated20–22. We address these questions by presenting the first experiment measuring anomalous weak values with just a single click, without the need for statistical averaging. The measurement uncertainty is significantly smaller than the gap between the measured weak value and the nearest eigenvalue. Beyond clarifying the meaning of weak values, demonstrating their non-statistical, single-particle nature, this result represents a breakthrough in understanding the foundations of quantum measurement, showing unprecedented measurement capability for further applications of weak values to quantum photonics.

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We propose an information-theoretic quantifier for the advantage gained from cooperation that captures the degree of dependency between subsystems of a global system. The quantifier is distinct from measures of multipartite correlations despite sharing many properties with them. It is directly computable for classical as well as quantum systems and reduces to comparing the respective conditional mutual information between any two subsystems. Exemplarily we show the benefits of using the new quantifier for symmetric quantum secret sharing. We also prove an inequality characterizing the lack of monotonicity of conditional mutual information under local operations and provide intuitive understanding for it. This underlines the distinction between the multipartite dependence measure introduced here and multipartite correlations.