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I came across a New Study at : http://arxiv.org/PS_cache/arxiv/pdf/1101/1101.2565v1.pdf . Which talks about Time like quantum entanglement. What does that mean?

Comment added by L.Motl: The same preprint has been discussed in this question and will be discussed in this question in the future.

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Please write timelike in one word, or at least use a hyphen. I keep misreading the title. –  Qmechanic Mar 30 '11 at 17:10

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The paper referenced in the question involves a transformation between Minkowski spacetime and Rindler spacetime. This is related in some ways to the question on entanglement or EPR pairs near a black hole horizon. An accelerated observer measure states in the region I they are causally connected to which are non-locally correlated across the event horizon into region II. This is similar to the black hole near horizon situation with quantum EPR pairs and states correlated from the exterior timelike region to the interior spacelike region. From the perspective of the Minkowski spacetime such spacelike correlations on the Rindler wedge are timelike.

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In most quantum field theories, operators localized at regions which are timelike separated don't commute. Not only that, the state at the earlier time can affect the state at the later time, meaning they are not causally independent. This means the relative states localized at timelike separated regions don't have a combined tensor product structure. Because of this, in most cases, it doesn't make any sense to speak of timelike entanglement.

However, for the special case of 1+1D with only massless fields, the only modes are left-movers and right-movers travelling at the speed of light. As a result, timelike separated regions are causally independent, and operators localized therein do actually commute. So, we can have timelike entanglement in this case, but it doesn't generalize.

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