PIRSA:17110058

Higher-order quantum computations and causal structures

APA

Perinotti, P. (2017). Higher-order quantum computations and causal structures. Perimeter Institute for Theoretical Physics. https://pirsa.org/17110058

MLA

Perinotti, Paolo. Higher-order quantum computations and causal structures. Perimeter Institute for Theoretical Physics, Nov. 21, 2017, https://pirsa.org/17110058

BibTex

          @misc{ scivideos_PIRSA:17110058,
            doi = {10.48660/17110058},
            url = {https://pirsa.org/17110058},
            author = {Perinotti, Paolo},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Higher-order quantum computations and causal structures},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2017},
            month = {nov},
            note = {PIRSA:17110058 see, \url{https://scivideos.org/index.php/pirsa/17110058}}
          }
          

Paolo Perinotti University of Pavia

Talk numberPIRSA:17110058
Source RepositoryPIRSA
Collection

Abstract

Conventional quantum processes are described by quantum circuits, that represent evolutions of states of systems from input to output. In this seminar we consider transformations of an input circuit to an output circuit, which then represent the transformation of quantum evolutions. At this level, all the processes complying to admissibility conditions have in principle a physical realization scheme. The construction of a hierarchy of transformations of transformations, however, can proceed arbitrarily far, and in the higher orders one encounters admissible functions that have indefinite causal structures. These give rise to questions about possible realization schemes. Still, many of the maps in the hierarchy can be proved to have a realistic physical interpretation. In order to study the hierarchy, we introduce a simple rule for constructing new types of maps from known ones, and show how the tensor product can be rephrased in terms of the new rule. We use the hierarchy of types to introduce a partial order, which allows us to prove properties of maps by induction. We will then use induction proofs to discuss the characterisation of mathematically admissible maps at every level. We show an important structural result for a subclass of higher-order maps, and we conclude with the open question of their physical achievability.