Quantum circuit complexity for linearly polarised light
Jean-Pierre Gazeau, Université Paris Cité
2024-12-13 godz. 9:45 - 11:15
I present a form of quantum circuit complexity that extends to open systems. To
illustrate the methodology, I focus on a basic model where the projective Hilbert
space of states is depicted by the set of orientations in the Euclidean plane.
Specifically, I investigate the dynamics of mixed quantum states as they undergo
interactions with a sequence of gates. This approach involves the analysis of
sequences of real 2X2 density matrices. Such a mathematical model is physically
exemplified by the Stokes density matrices, which delineate the linear polarisation of
a quasi-monochromatic light beam, and the gates, which are viewed as quantum
polarisers, whose states are also real 2X2 density matrices. The interaction between
polariser-linearly polarised light is construed à la Von Neumann within the context of
this quantum formalism. Each density matrix for the light evolves in a way
analogous to a Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) process during the
time interval between consecutive gates. Notably, when considering an upper limit
for accuracy, it is shown that the optimal number of gates follows a power-law
relationship.
From a submitted article co-authored by E. Curado A. Maioli, D. Noguera (CBPF,
Rio), S. Faci (UFF, Rio), T. Koide (UFRJ, Rio).
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