Towards the identification of Quantum Theory: Operational Approach


Saha, S. (2023). Towards the identification of Quantum Theory: Operational Approach. Perimeter Institute. https://pirsa.org/23010109


Saha, Sutapa. Towards the identification of Quantum Theory: Operational Approach. Perimeter Institute, Jan. 19, 2023, https://pirsa.org/23010109


          @misc{ pirsa_23010109,
            doi = {10.48660/23010109},
            url = {https://pirsa.org/23010109},
            author = {Saha, Sutapa},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Towards the identification of Quantum Theory: Operational Approach},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {jan},
            note = {PIRSA:23010109 see, \url{https://pirsa.org}}

Sutapa Saha Indian Statistical Institute


In spite of its immense importance in the present-day information technology, the foundational aspects of quantum theory (QT) remain still elusive. In particular, there is no such set of physically motivated axioms which can answer why Hilbert space formalism is the only natural choice to describe the microscopic world. Hence, to shed light on the unique formalism of QT, two different operational frameworks will be described in the primitive of various convex operational theories. The first one refers to a kinematical symmetry principle which would be proposed from the perspective of single copy state discrimination and it would be shown that this symmetry holds for both classical and QT – two successful descriptions of the physical world. On the other hand, studying a wide range of convex operational theories, namely the General Probabilistic Theories (GPTs) with polygonal state spaces, we observe the absence of such symmetry. Thus, the principle deserves its own importance to mark a sharp distinction between the physical and unphysical theories. Thereafter, a distributed computing scenario will be introduced for which the other convex theories except the QT turn out to be equivalent to the classical one even though the theories possess more exotic state and effect spaces. We have coined this particular operational framework as ‘Distributed computation with limited communication’ (DCLC). Furthermore, it will be shown that the distributed computational strength of quantum communication will be justified in terms of a stronger version of this task, namely the ‘Delayed choice distributed computation with limited communication’ (DC2LC). The proposed task thus provides a new approach to operationally single out quantum theory in the theory-space and hence promises a novel perspective towards the axiomatic derivation of Hilbert space quantum mechanics.

Phys. Rev. A (Rapid)100, 060101 (2019)
Ann. Phys.(Berlin)2020,532, 2000334 (2020)
arXiv:2012.05781 [quant-ph](2020)

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