Experiments towards Falsification of Noncontextual Hidden Variable Theories

Abstract

We present two experiments testing the hypothesis of noncontextual hidden variables (NCHV's). The first one is based on observation of two-photon pseudo-Greenberger-Horne-Zeilinger correlations, with two of the originally three particles mimicked by the polarization degree of freedom and the spatial degree of freedom of a single photon. The second one, a single-photon experiment, utilizes the same trick to emulate two particle correlations, and is an "event ready" test of a Bell-like inequality, derived from the noncontextuality assumption. Modulo fair sampling, the data falsify NCHV's.The statistical nature of quantum predictions has frequently initiated efforts to expand the quantum mechanical description. The so-called hidden variable concepts try to cure the quantum indeterminism by ascribing values to the properties of a system which are defined already prior to the measurement. The question arises whether such expansion of the theory is justified.noncontextual hidden variable (NCHV) theories assume that the predetermined result of a particular measurement does not depend on what other observable is simultaneously measured (see e.g. [1]). Such cryptodeterminism was ruled out by the Bell-Kochen-Specker (BKS) theorem [2], which, as a mathematical theorem, does not need experimental confirmation -and neither suggests one. Yet, quite recently, doubts arose about the usefullness of the BKS theorem due to the impossibility of experimentally testing the yes/no contradiction of the BKS theorem in real world, where one is always confined to finite measurement times and precision [3]. NCHV theories form a subset of local realistic hidden variable (LHV) theories, which rely on the more plausible assumption that the predetermined result of a particular measurement does not depend on what other observable is simultaneously measured in a spatially separated region. Bell's theorem [4] gives a clear prescription for a statistical test of LHV theories. However, almost all experiments testing LHV theories do not enforce spacelike separation of measurements, and all are plagued with the low detection efficiency, thus falling short of definitely invalidating LHV theories [5].We report two experiments testing the validity of NCHV theories. The experiments are much simpler than equivalent Bell tests (with no strict imposition of locality), and much less sensitive to experimental imperfections. This includes lower threshold interference visibility and consequently also less demanding threshold for detection efficiencies. The possible adaptation to other quantum systems paves the way to a loophole-free test of the particular class of noncontextual hidden variable theories. Formally, the experiments are employing the fact, that measurements on distinct tensor product factors of Hilbert space commute and can therefore form varying contexts for one another. In the analysis of these experiments we obtain, for a specific state [6], verifiable, statistical conditions for the measurement results. In the first experiment the three particl...

Compatibility and noncontextuality for sequential measurements

“…Experimental tests of noncontextual HV theories have been carried out with photons [35][36][37][38]46], neutrons [37,38], lasercooled trapped ions [45], and liquid-state nuclear magnetic resonance systems [48]. In the experiments with photons and neutrons, single particles were prepared and measured in a four-dimensional state space composed of two twodimensional state spaces describing the particle's polarization and the path it was following.…”

“…Nevertheless, first experiments have been performed, but these experiments required some additional assumptions [35][36][37][38]. Furthermore, the notion of contextuality has been extended to state preparations [39] and experimentally investigated [40].…”

Single-particle nonlocality and entanglement with the vacuum

“…Nonlocal properties of a single particle have been discussed by several authors [15,16,17,18,19,20,21,22]. However, most of the proposals have been (or can be) criticized for various reasons.…”

“…In the experiment proposed by Gerry [21] the nonlocal properties of a single photon are transferred to two atoms prior to the measurement and, therefore, what is finally measured are the correlations between two particles, which makes the claim of single-particle nonlocality somewhat weaker. To the best of our knowledge, only one experiment has hitherto been performed that claims to be a single-particle test of noncontextual hidden variables [22], but, unfortunately, it is also based on self-interference in a Mach-Zehnder interferometer. Thus, one can conclude that so far no loophole free demonstration of single-particle nonlocality has been performed.…”

Quantum nonlocality and applications in quantum-information processing of hybrid entangled states

“…However, this is not the case for the trapped-ion system, where entanglement occurs between two different degrees of freedom of a single ion and as such, the space-like separation can not be achieved. Thus for the latter system, it will be more appropriate to consider quantum contextuality [32][33][34]. Non-contextual hidden variable theories predict that the value of an observable is predetermined and thus independent on the experimental context, i.e., what other comeasurable observable is simultaneously measured, and whether or not the space-like separation condition is fulfilled.…”