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For example, suppose an entangled electron and anti-electron have been produced in an inertial center-of-mass frame. If we have just a single detector and it observes a positron, then it's probably from such a pair. But does anything about the positron other than its rarity suggest that it is entangled, if we do not also observe the other particle of the pair?

Tobias Fünke
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Richard D-W
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1 Answers1

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Let V and W be the state spaces of the individual particles. An observable G acting on V acts on $V\otimes W$ by acting on the first factor, and it's easy to check that the eigenspaces are all of the form $H\otimes W$ where $H$ is an eigenspace of G acting on V. So nothing in the outcome of a measurement of G can reveal the entanglement.

WillO
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