Contributor info: Dr Kavan Modi

Maxwell West, Neil Dowling, Angus Southwell, Martin Sevior, Muhammad Usman, Kavan Modi, Thomas Quella

SciPost Phys. Core 8, 081 (2025) · published 10 November 2025 | Toggle abstract · pdf

There has recently been considerable interest in studying quantum systems via dynamical Lie algebras (DLAs) – Lie algebras generated by the terms which appear in the Hamiltonian of the system. However, there are some important properties that are revealed only at a finer level of granularity than the DLA. In this work we explore, via the commutator graph, average notions of scrambling, chaos and complexity over ensembles of systems with DLAs that possess a basis consisting of Pauli strings. Unlike DLAs, commutator graphs are sensitive to short-time dynamics, and therefore constitute a finer probe to various characteristics of the corresponding ensemble. We link graph-theoretic properties of the commutator graph to the out-of-time-order correlator (OTOC), the frame potential, the frustration graph of the Hamiltonian of the system, and the Krylov complexity of operators evolving under the dynamics. For example, we reduce the calculation of average OTOCs to a counting problem on the graph; separately, we connect the Krylov complexity of an operator to the module structure of the adjoint action of the DLA on the space of operators in which it resides, and prove that its average over the ensemble is lower bounded by the average shortest path length between the initial operator and the other operators in the commutator graph.

Neil Dowling, Pedro Figueroa-Romero, Felix A. Pollock, Philipp Strasberg, Kavan Modi

SciPost Phys. Core 6, 043 (2023) · published 14 June 2023 | Toggle abstract · pdf

A generic non-integrable (unitary) out-of-equilibrium quantum process, when interrogated across many times, is shown to yield the same statistics as an (non-unitary) equilibrated process. In particular, using the tools of quantum stochastic processes, we prove that under loose assumptions, quantum processes equilibrate within finite time intervals. Sufficient conditions for this to occur are that multitime observables are coarse grained in both space and time, and that the initial state overlaps with many different energy eigenstates. These results help bridge the gap between (unitary) quantum and (non-unitary) statistical physics, i.e., when all multitime properties and correlations are well approximated by stationary quantities, which includes non-Markovianity and temporal entanglement. We discuss implications of this result for the emergence of classical stochastic processes from multitime measurements of an underlying genuinely quantum system.

Felix A. Pollock, Emanuel Gull, K. Modi, Guy Cohen

SciPost Phys. 13, 027 (2022) · published 18 August 2022 | Toggle abstract · pdf

We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they can be difficult to formulate for observables spanning the system and its environment, such as those characterizing transport properties. A large variety of mixed system--environment observables, as well as their statistical properties, can be evaluated by considering counting fields. Given a numerical method able to simulate the field-modified dynamics over the memory timescale, we show that the long-lived full counting statistics can be efficiently obtained from the reduced dynamics. We demonstrate the utility of the technique by computing the long-time current in the nonequilibrium Anderson impurity model from short-time Monte Carlo simulations.

Simon Milz, Cornelia Spee, Zhen-Peng Xu, Felix A. Pollock, Kavan Modi, Otfried Gühne

SciPost Phys. 10, 141 (2021) · published 11 June 2021 | Toggle abstract · pdf

While spatial quantum correlations have been studied in great detail, much less is known about the genuine quantum correlations that can be exhibited by temporal processes. Employing the quantum comb formalism, processes in time can be mapped onto quantum states, with the crucial difference that temporal correlations have to satisfy causal ordering, while their spatial counterpart is not constrained in the same way. Here, we exploit this equivalence and use the tools of multipartite entanglement theory to provide a comprehensive picture of the structure of correlations that (causally ordered) temporal quantum processes can display. First, focusing on the case of a process that is probed at two points in time -- which can equivalently be described by a tripartite quantum state -- we provide necessary as well as sufficient conditions for the presence of bipartite entanglement in different splittings. Next, we connect these scenarios to the previously studied concepts of quantum memory, entanglement breaking superchannels, and quantum steering, thus providing both a physical interpretation for entanglement in temporal quantum processes, and a determination of the resources required for its creation. Additionally, we construct explicit examples of W-type and GHZ-type genuinely multipartite entangled two-time processes and prove that genuine multipartite entanglement in temporal processes can be an emergent phenomenon. Finally, we show that genuinely entangled processes across multiple times exist for any number of probing times.