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Physical Review A

Violation of an extended Wigner inequality with high-angular-momentum states

William N. Plick, Robert Fickler, Radek Łapkiewicz, Sven Ramelow

Published Feb 27, 2015• 1 citation
Publisher

Abstract

In the study of systems that cannot be described classically, the Wigner inequality, has received only a small amount of attention. In this paper we extend the Wigner inequality---originally derived in 1969---and show how it may be used to contradict local realism with only coincidence detections in the absence of two-outcome measurements---that is, for any system where only one possible result of a pair of potential outcomes can be registered. It thus encapsulates a much broader class of measurement schemes than could previously violate a local-realistic inequality. This is possible due to an assumption of ``extended fairness'' on the measurement outcomes, which we posit is highly plausible. We then apply this inequality to a recently constructed setup with access to entangled pairs of photons with very high angular momenta, in which no previously derived local-realistic inequality could successfully be used without making very broad assumptions. We thus demonstrate the versatility of this inequality under very lossy conditions.

DOI
10.1103/physreva.91.022124

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In the study of systems that cannot be described classically, the Wigner inequality, has received only a small amount of attention. In this paper we extend the Wigner inequality---originally derived in 1969---and show how it may be used to contradict local realism with only coincidence detections in the absence of two-outcome measurements---that is, for any system where only one possible result of a pair of potential outcomes can be registered. It thus encapsulates a much broader class of measurement schemes than could previously violate a local-realistic inequality. This is possible due to an assumption of ``extended fairness'' on the measurement outcomes, which we posit is highly plausible. We then apply this inequality to a recently constructed setup with access to entangled pairs of photons with very high angular momenta, in which no previously derived local-realistic inequality could successfully be used without making very broad assumptions. We thus demonstrate the versatility of this inequality under very lossy conditions.
In the study of systems that cannot be described classically, the Wigner inequality, has received only a small amount of attention. In this paper we extend the Wigner inequality - originally derived in 1969 - and show how it may be used to contradict local realism with only coincidence detections in the absence of two-outcome measurements - that is, for any system where only one possible result of a pair of potential outcomes can be registered. It thus encapsulates a much broader class of measurement schemes than could previously violate a local-realistic inequality. This is possible due to an assumption of "extended fairness" on the measurement outcomes, which we posit is highly plausible. We then apply this inequality to a recently constructed setup with access to entangled pairs of photons with very high angular momenta, in which no previously derived local-realistic inequality could successfully be used without making very broad assumptions. To our knowledge this experiment constitutes a violation of local realism with the largest quanta to date. We thus demonstrate the versatility of this inequality under very lossy conditions.
In the study of systems that can not be explained classically, the Wigner inequality, has received only a small amount of attention. In this paper we extend the Wigner inequality - originally derived in 1969 - and show how it may be used to contradict local realism with only coincidence detections in the absence of two-outcome measurements - that is, any system where only one possible result of a pair of potential outcomes can be registered. This encapsulates a much broader class of measurement schemes than could previously violate a local-realistic inequality. We then apply this inequality to a recently constructed setup with access to entangled pairs of photons with very high angular momenta, in which no previously derived local-realistic inequality could successfully be used without making very broad assumptions. This experiment constitutes the first violation of local realism with such high quanta. We thus demonstrate the versatility of this inequality under very lossy conditions.
We present a novel Bell inequality that does not require dichotomic (two-outcome) measurements. It is based on an inequality originally derived by Wigner in 1969, extending it such that no assumptions other than local-realism, fair-sampling, and freedom-of-choice are necessary. It is most useful in situations where there is no direct access to true two-outcome (dichotomic) measurements, like photonic quantum experiments where spatial degrees-of-freedoms are often analyzed with spatial light modulators (SLMs), as well as many other experimental scenarios. The only other class of inequalities (CH-type) that has this feature requires coincidence and single count-rates to be of the same order of magnitude for violation, ours does not. It thereby enables the stringent verification of entanglement and rejection of local-realism, without any assumptions about the underlying Hilbert-space, such as dimensionality – in the most dificult experimental conditions. We also experimentally violate this inequality in a novel setup: entangled states of very high orbital angular momentum. This constitutes a rejection of the hypothesis of local realism (under reasonable assumptions) with the highest quanta to date.
We propose a Wigner-like inequality suitable for testing the hypothesis of realism. We show that this inequality is identical neither to the well-known Wigner inequality nor to the Leggett-Garg inequality in Wigner form. The obtained inequality is suitable for testing realism not only in quantum mechanical systems, but also in quantum field systems. Also we propose a mathematically consistent derivation of the Leggett-Garg inequality in Wigner form, which was recently presented in the literature, for three and nnn distinct moments of time. Contrary to these works, our rigor derivation uses Kolmogorov axiomatics of probability theory. We pay special attention to the construction and studies of the spaces of elementary outcomes. Based on the Leggett-Garg inequality in Wigner form for nnn distinct moments of time we prove that any unitary evolution of a quantum system contradicts the concept of macroscopic realism. We show that application of the concept of macroscopic realism to any quantum system leads to ``freezing'' of the system in the initial state. It is shown that for a particle with an infinite number of observables the probability to find a pair of the observables in some defined state is zero, even if the operators of these observables commute. This fact might serve as an additional logical argument for the contradiction between quantum theory and classical realism.
In a local realist model, physical properties are defined prior to and independent of measurement and no physical influence can propagate faster than the speed of light. Proper experimental violation of a Bell inequality would show that the world cannot be described with such a model. Experiments intended to demonstrate a violation usually require additional assumptions that make them vulnerable to a number of ``loopholes.'' In both pulsed and continuously pumped photonic experiments, an experimenter needs to identify which detected photons belong to the same pair, giving rise to the coincidence-time loophole. Here, via two different methods, we derive Clauser-Horne- and Eberhard-type inequalities that are not only free of the fair-sampling assumption (thus not being vulnerable to the detection loophole), but also free of the fair-coincidence assumption (thus not being vulnerable to the coincidence-time loophole). Both approaches can be used for pulsed as well as for continuously pumped experiments. Moreover, as they can also be applied to already existing experimental data, we finally show that a recent experiment [Giustina et al., Nature (London) 497, 227 (2013)] violated local realism without requiring the fair-coincidence assumption.