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Physical Review Letters

Observing Local Realism Violations with a Combination of Sensitive and Insensitive Detectors

Bernard Yurke, David Stoler

Published Dec 22, 1997• 27 citations
Publisher

Abstract

Several systems are exhibited in which the establishment of local realism violation is achieved even when some of the detectors employed are insensitive. The insensitive detectors are homodyne detectors whose task is to determine if the amplitude of a coherent state is $\ensuremath{\alpha}$ or $\ensuremath{-}\ensuremath{\alpha}$. This determination can be achieved with low quantum efficiency detectors when $|\ensuremath{\alpha}|$ is large. The other detectors employed determine whether there is an even number or an odd number of photons in a state. These detectors are sensitive since they are required to resolve the difference of one photon. For the examples given, the local realism violation is not diminished as $|\ensuremath{\alpha}|$ is increased.

DOI
10.1103/physrevlett.79.4941

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Several systems are exhibited in which the establishment of local realism violation is achieved even when some of the detectors employed are insensitive. The insensitive detectors are homodyne detectors whose task is to determine if the amplitude of a coherent state is \ensuremathα\ensuremath{\alpha}\ensuremathα or \ensuremath−\ensuremathα\ensuremath{-}\ensuremath{\alpha}\ensuremath−\ensuremathα. This determination can be achieved with low quantum efficiency detectors when ∣\ensuremathα∣|\ensuremath{\alpha}|∣\ensuremathα∣ is large. The other detectors employed determine whether there is an even number or an odd number of photons in a state. These detectors are sensitive since they are required to resolve the difference of one photon. For the examples given, the local realism violation is not diminished as ∣\ensuremathα∣|\ensuremath{\alpha}|∣\ensuremathα∣ is increased.
We show that it is, in principle, possible to perform local-realism violating experiments of the Hardy type in which only position and momentum measurements are made on two particles emanating from a common source. In the optical domain, homodyne detection of the in-phase and out-of-phase amplitude components of an electromagnetic field is analogous to position and momentum measurement. Hence, local realism violations of the Hardy type are possible in optical systems employing only homodyne detection.
Tests of local realism and their applications aim for very high confidence in their results even in the presence of potentially adversarial effects. For this purpose, one can measure a quantity that reflects the amount of violation of local realism and determine a bound on the probability, according to local realism, of obtaining a violation at least that observed. In general, it is difficult to obtain sufficiently robust and small bounds. Here we describe an efficient protocol for computing such bounds from any set of Bell inequalities for any number of parties, measurement settings, or outcomes. The protocol can be applied to tests of other properties (such as entanglement or dimensionality) that are witnessed by linear inequalities.