Causal Constraints on Possible Measurements


Borsten, L. (2012). Causal Constraints on Possible Measurements. Perimeter Institute. https://pirsa.org/12060078


Borsten, Leron. Causal Constraints on Possible Measurements. Perimeter Institute, Jun. 28, 2012, https://pirsa.org/12060078


          @misc{ pirsa_PIRSA:12060078,
            doi = {10.48660/12060078},
            url = {https://pirsa.org/12060078},
            author = {Borsten, Leron},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Causal Constraints on Possible Measurements},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {jun},
            note = {PIRSA:12060078 see, \url{https://pirsa.org}}

Leron Borsten Heriot-Watt University


A crucial question in any approach to quantum information processing is:  first, how are classical bits encoded physically in the quantum system, second, how are they then manipulated and, third,  how are they finally read out?   These 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. 

Motivated 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.