Restrictions on realizable unitary operations imposed by symmetry and locality

ABSTRACT According to a fundamental result in quantum computing, any unitary transformation on a composite system can be generated using so-called 2-local unitaries that act only on two

subsystems. Beyond its importance in quantum computing, this result can also be regarded as a statement about the dynamics of systems with local Hamiltonians: although locality puts various

constraints on the short-term dynamics, it does not restrict the possible unitary evolutions that a composite system with a general local Hamiltonian can experience after a sufficiently long

time. Here we show that this universality does not remain valid in the presence of conservation laws and global continuous symmetries such as U(1) and SU(2). In particular, we show that

generic symmetric unitaries cannot be implemented, even approximately, using local symmetric unitaries. Based on this no-go theorem, we propose a method for experimentally probing the

locality of interactions in nature. In the context of quantum thermodynamics, our results mean that generic energy-conserving unitary transformations on a composite system cannot be realized

solely by combining local energy-conserving unitaries on the components. We show how this can be circumvented via catalysis. Access through your institution Buy or subscribe This is a

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Yunger-Halpern for reading the manuscript carefully and providing many useful comments. This work was supported by NSF FET-1910571, NSF Phy-2046195 and Army Research Office

(W911NF-21-1-0005). AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Departments of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA Iman Marvian Authors * Iman

Marvian View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS I.M. was the sole contributor to all aspects of this work. CORRESPONDING AUTHOR

Correspondence to Iman Marvian. ETHICS DECLARATIONS COMPETING INTERESTS The author declares no competing interest. PEER REVIEW INFORMATION _Nature Physics_ thanks Álvaro Alhambra and the

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THIS ARTICLE CITE THIS ARTICLE Marvian, I. Restrictions on realizable unitary operations imposed by symmetry and locality. _Nat. Phys._ 18, 283–289 (2022).

https://doi.org/10.1038/s41567-021-01464-0 Download citation * Received: 17 January 2021 * Accepted: 12 November 2021 * Published: 10 January 2022 * Issue Date: March 2022 * DOI:

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