Quantum-Classical Hybrid Systems And Their Quasifree Transformations

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Lars Dammeier and Reinhard F. Werner

Institut für Theoretische Physik, Leibniz Universität Hannover, Germany

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Abstract

We study continuous variable systems, in which quantum and classical degrees of freedom are combined and treated on the same footing. Thus all systems, including the inputs or outputs to a channel, may be quantum-classical hybrids. This allows a unified treatment of a large variety of quantum operations involving measurements or dependence on classical parameters. The basic variables are given by canonical operators with scalar commutators. Some variables may commute with all others and hence generate a classical subsystem. We systematically study the class of “quasifree” operations, which are characterized equivalently either by an intertwining condition for phase-space translations or by the requirement that, in the Heisenberg picture, Weyl operators are mapped to multiples of Weyl operators. This includes the well-known Gaussian operations, evolutions with quadratic Hamiltonians, and “linear Bosonic channels”, but allows for much more general kinds of noise. For example, all states are quasifree. We sketch the analysis of quasifree preparation, measurement, repeated observation, cloning, teleportation, dense coding, the setup for the classical limit, and some aspects of irreversible dynamics, together with the precise salient tradeoffs of uncertainty, error, and disturbance. Although the spaces of observables and states are infinite dimensional for every non-trivial system that we consider, we treat the technicalities related to this in a uniform and conclusive way, providing a calculus that is both easy to use and fully rigorous.

► BibTeX data

@article{Dammeier2023quantumclassical, doi = {10.22331/q-2023-07-26-1068}, url = {https://doi.org/10.22331/q-2023-07-26-1068}, title = {Quantum-{C}lassical {H}ybrid {S}ystems and their {Q}uasifree {T}ransformations}, author = {Dammeier, Lars and Werner, Reinhard F.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1068}, month = jul, year = {2023}<br /> }

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Cited by

[1] Alberto Barchielli and Reinhard Werner, “Hybrid quantum-classical systems: Quasi-free Markovian dynamics”, arXiv:2307.02611, (2023).

[2] Lauritz van Luijk, René Schwonnek, Alexander Stottmeister, and Reinhard F. Werner, “The Schmidt rank for the commuting operator framework”, arXiv:2307.11619, (2023).

[3] Lauritz van Luijk, Alexander Stottmeister, and Reinhard F. Werner, “Convergence of Dynamics on Inductive Systems of Banach Spaces”, arXiv:2306.16063, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-07-26 22:31:17). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2023-07-26 22:31:16).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2023-07-26-1068/

Time Stamp: July 26, 2023

Time Stamp: Feb 12, 2024

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