Hi all,
This week we will have another QIT seminar on Friday by our visitor Lorenzo Guglielmi, who will talk about “Introduction to p-adic Quantum Mechanics: towards p-adic entanglement”. The talk will take place at 15:30 in HIT E41.1.
Next week, on Monday, Joshua Laux will talk about “Agent-Like Observers in Extended Wigner’s Friend Scenarios on Quantum Computers”. The talk will take place at 15:00 in HIT E41.1.
See below for the abstracts.
Best,
Ladina
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Title:
Introduction to p-adic Quantum Mechanics: towards p-adic entanglement
Abstract:
At the present time, many physicists believe that quantum mechanics and general relativity are unfit to describe a wide range of physical phenomena related to the ultimate structure of matter and space-time at a scale comparable to Planck’s length.It seems, therefore, necessary to find new theoretical schemes, and according to Dirac’s view of modern physics, it is likely that the identification of the right mathematical framework for these new physical models will play a major role. At the end of the last century, Volovich and Vladimirov envisaged a description of microscopic phenomena based on a new picture of space-time at Planck’s scale. This description stemmed from the fundamental observation that if Planck’s length is assumed to be the smallest measurable length, then space-time should possess a non-Archimedean character.Pursuing this idea to its logical conclusions, one is led to the further observation that the only complete non-Archimedean field one can construct starting from the field of rational numbers is, up to isomorphisms, the field of p-adic numbers on
Q
p
, where p is a generic prime number. It is then natural to attempt at developing p-adic models of quantum theory and formulating field theories on
Q
p
.
We introduce the mathematical physics foundations of p-adic quantum mechanics following the same route as the standard von Neumann algebraic formulation of quantum mechanics. After recalling the basic knowledge of p-adic numbers and their extensions, we also define p-adic Hilbert spaces, adjointable operators, trace-class operators, statistical states, and self-adjoint-operator-valued measures, which provide a non-Archimedean analogue of the standard framework. The main focus is on the construction of the tensor products of p-adic Hilbert spaces. We consider the algebraic tensor product of p-adic Hilbert spaces and then define a suitable norm on this linear space. It turns out that, in the p-adic framework, this norm is the analogue of the projective norm associated with the tensor product of real or complex normed spaces. By metrically completing the resulting p-adic normed space, and equipping it with a suitable inner product, we yield the result. That this is indeed the correct p-adic counterpart of the tensor product of complex Hilbert spaces is also certified by establishing a natural isomorphism between this p-adic Hilbert space and the corresponding Hilbert–Schmidt class. These findings provide us with the mathematical foundations necessary to explore quantum entanglement in the p-adic setting, with potential applications in the emerging field of p-adic quantum information theory.
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Title:
Agent-Like Observers in Extended Wigner’s Friend Scenarios on Quantum Computers
Abstract:
Extended Wigner’s Friend scenarios raise fundamental questions about applying quantum theory to systems that include observers. Within the framework of Local Friendliness, these questions can be formulated as experimentally testable inequalities derived from assumptions about observed events and local agency.
This presentation discusses first steps towards implementing more structured, agent-like systems as the “friend” in such scenarios. Simple agents are realized as reversible quantum circuits and embedded into a one-friend Extended Wigner’s Friend experiment. Their behavior and the resulting Local Friendliness violations are investigated using ideal simulations, noise models, and IBM quantum hardware. The results demonstrate the feasibility of introducing explicit agent functionality into these experiments while highlighting the limitations of current quantum hardware.