Causal Constraints on Possible Measurements

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crucial question in any approach to quantum information processing
is:  first, how are classical bits

physically in the quantum system, second, how are they then manipulated and,
third,  how are they finally read out?


questions are particularly challenging when investigating quantum
information processing in a relativistic spacetime. An obvious
framework for such an investigation is relativistic quantum field
theory.  Here, progress is hampered by the lack of a universally
applicable rule for calculating the probabilities of the outcomes of ideal
measurements on a relativistic quantum field in a collection of spacetime
regions. Indeed,
a straightforward relativistic generalisation of the non-relativistic formula
for these probabilities leads to superluminal signalling. 

by these considerations we ask what interventions/ideal measurements can we in
principle make, taking  causality as our guiding criterion. In the course
of this analysis we reconsider various aspects of ideal measurements in QFT,
detector models and the probability rules themselves. In particular, it is
shown that an ideal measurement of a one–particle wave packet state of a
relativistic quantum field in Minkowski spacetime enables superluminal
signalling. The result holds for a measurement that takes place over an
intervention region in spacetime whose extent in time in some frame is longer
than the light crossing time of the packet in that frame.