Resource theory of quantum uncomplexity - Kölner UniversitätsPublikationsServer

Halpern, Nicole Yunger, Kothakonda, Naga B. T., Haferkamp, Jonas, Munson, Anthony, Eisert, Jens ORCID: 0000-0003-3033-1292 and Faist, Philippe (2022). Resource theory of quantum uncomplexity. Phys. Rev. A, 106 (6). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2469-9934

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DOI:10.1103/PhysRevA.106.062417

Abstract

Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the state from a simple tensor product. The greater a state's distance from maximal complexity, or uncomplexity, the more useful the state is as input to a quantum computation. Separately, resource theories-simple models for agents subject to constraints-are burgeoning in quantum information theory. We unite the two domains, confirming Brown and Susskind's conjecture that a resource theory of uncomplexity can be defined. The allowed operations, fuzzy operations, are slightly random implementations of two-qubit gates chosen by an agent. We formalize two operational tasks, uncomplexity extraction and expenditure. Their optimal efficiencies depend on an entropy that we engineer to reflect complexity. We also present two monotones, uncomplexity measures that decline monotonically under fuzzy operations, in certain regimes. This work unleashes on many-body complexity the resource-theory toolkit from quantum information theory.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Halpern, Nicole Yunger	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Kothakonda, Naga B. T.	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Haferkamp, Jonas	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Munson, Anthony	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Eisert, Jens	UNSPECIFIED	orcid.org/0000-0003-3033-1292	UNSPECIFIED
Faist, Philippe	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED