Jens Eisert

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In this talk, we revisit the notions of entanglement, information, and
complexity in quantum systems from a somewhat unconventional perspective —
by placing the observer of a phenomenon at the center and adopting a
strictly operational viewpoint. We begin by examining the precise ways in
which entanglement and complexity in random quantum circuits are connected
[1–3]. Along the way, we discuss random tensor networks as a powerful tool
for advancing our understanding of complex quantum systems [4]. We show
that the average-case time evolution of interacting quantum systems can, in
a well-defined sense to be explained, be surprisingly uncomplex — despite
the fact that time evolution under local Hamiltonians is BQP-complete [5].
Building on this, we demonstrate that entanglement theory is fundamentally
altered once one accepts that all implemented operations must be both
computationally and sample efficient [6]. Pushing the operational
perspective further, we reveal that certain systems are not quantum
chaotic, even though no polynomially bounded observer can distinguish them
from Gaussian unitary ensembles, which paradigmatically represent
quantum-chaotic systems [7]. We conclude by reflecting on the role of the
observer — who gathers data and acts operationally efficiently — in shaping
our understanding of entanglement, information, and complexity.

[1] Nature Physics 18, 528 (2022).
[2] Physical Review Letters 127, 020501 (2021).
[3] PRX Quantum 6, 010346 (2025).
[4] arXiv:2508.16570 (2025).
[5] Nature Physics 20, 1401 (2024).
[6] Nature Physics, online (2025).
[7] arXiv:2410.18196 (2024).

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Free University Berlin
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Contact: Sebastian Diehl, Simon Trebst