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

Abstract

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...

Footprints of quantum pigeons

“…A proper implementation of the example [4] requires the measurement of nonlocal variables like parity [13]. For example, the setup of the recent implementation [14] of nonlocal measurement [15] could allow a more satisfactory experiment showing the failure of the pigeonhole principle in the version with "holes" still being spin states. Indeed, in [14] there was the experimental realization of a pre-and postselected pair of particles fulfilling a requirement similar to the type we are looking for: σ (j)…”

“…Thus, one could directly measure the needed negative parities, corresponding to σ (j) z σ (k) z = −1, for randomly chosen pairs of pre-and postselected transmons. This experiment will have a conceptual advantage relative to [14] since here the pointer is an external measuring device, and not another degree of the measured photons. Figure 1 illustrates how to implement the needed parity measurements for the quantum pigeonhole paradox with superconducting transmons.…”

The problem of connection of observer’s mind with quantum-mechanical description of physical reality

“…Впервые такие эксперименты были проведены Алленом Аспе в 1980-х годах, затем успешно повторены рядом других исследователей. Это означает, что привычное представление о динамических свойствах квантовой частицы, реально существующих ещё до измерения и наблюдаемых при измерении, неверно [39]. Кроме того, следует принимать во внимание то, что волновая функция -это, в принципе, не сам процесс, а лишь его вероятность.…”

“…В 2016 году Эдриан Кент, профессор квантовой физики из Кембриджского университета Великобритании, один из самых уважаемых квантовых философов, осторожно предположил, что сознание может менять поведение квантовых систем [39]. Однако, по мнению Кента, проблема состоит в том, что из квантовой теории невозможно извлечь теорию сознания, поскольку невозможно вывести описание самого сознания и его свойств.…”

“…Эдриан Кент полагает, что такие проявления можно получить экспериментально. Шансы на их нахождение он оптимистично оценивает приблизительно на 15%, а это совсем немало для рационального материалиста [28,39]. Более того, Кент утверждает, что с небольшой долей вероятности в 3% мы получим эти данные уже в ближайшие 50 лет.…”