Open Access

ARTICLE

On the Validity of Intermediate Tracing in Multiple Quantum Interactions

Reuven Ianconescu^1,2,*, Bin Zhang^1,3, Aharon Friedman⁴, Jacob Scheuer^1,5, Avraham Gover^1,5

1 School of Electrical Engineering-Physical Electronics, Tel Aviv University, Ramat Aviv, Israel
2 Department of Electrical Engineering, Shenkar College of Engineering and Design, Anna Frank 12, Ramat Gan, Israel
3 State Key Laboratory of Quantum Functional Materials, School of Physical Science and Technology and Center for Transformative Science, ShanghaiTech University, Shanghai, China
4 Schlesinger Family Accelerator Centre, Ariel University, Ariel, Israel
5 Center for Light-Matter Interaction, Tel Aviv University, Ramat Aviv, Israel

* Corresponding Author: Reuven Ianconescu. Email:

Journal of Quantum Computing 2026, 8, 1-11. https://doi.org/10.32604/jqc.2026.076154

Received 15 November 2025; Accepted 23 January 2026; Issue published 27 February 2026

Abstract

Interactions between many (initially separate) quantum systems raise the question on how to prepare and how to compute the measurable results of their interaction. When one prepares each system individually and let them interact, one has to tensor multiply their density matrices and apply Hamiltonians on the composite system (i.e., the system which includes all the interacting systems) for definite time intervals. Evaluating the final state of one of the systems after multiple consecutive interactions requires tracing all other systems out of the composite system, which may grow to immense dimensions. For computational efficiency during the interaction(s), one may consider only the contemporary interacting partial systems, while tracing out the other non-interacting systems. In concrete terms, the type of problems to which we direct this formulation is a “target” system interacting successively with “incident” systems, where the “incident” systems do not mutually interact. For example, a two-level atom interacting successively with free electrons, or a resonant cavity interacting with radiatively free electrons, or a quantum dot interacting successively with photons. We refer to a “system” as one of the components before interaction, while each interaction creates a “composite system”. A new interaction of the “composite system” with another “system” creates a “larger composite system”, unless we trace out one of the systems before this interaction. The scope of this work is to show that under proper conditions, one may add a system to the composite system just before it interacts, and one may trace out this very system after it finishes interacting. We show in this work a mathematical proof of the above property and give a computational example.

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