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Zhu, Huangjun, Hayashi, Masahito and Chen, Lin (2018). Axiomatic and operational connections between the l(1)-norm of coherence and negativity. Phys. Rev. A, 97 (2). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2469-9934

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Abstract

Quantum coherence plays a central role in various research areas. The l(1)-norm of coherence is one of the most important coherence measures that are easily computable, but it is not easy to find a simple interpretation. We show that the l(1)-norm of coherence is uniquely characterized by a few simple axioms, which demonstrates in a precise sense that it is the analog of negativity in entanglement theory and sum negativity in the resource theory of magic-state quantum computation. We also provide an operational interpretation of the l(1)-norm of coherence as the maximum entanglement, measured by the negativity, produced by incoherent operations acting on the system and an incoherent ancilla. To achieve this goal, we clarify the relation between the l(1)-norm of coherence and negativity for all bipartite states, which leads to an interesting generalization of maximally correlated states. Surprisingly, all entangled states thus obtained are distillable. Moreover, their entanglement cost and distillable entanglement can be computed explicitly for a qubit-qudit system.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Zhu, Huangjun UNSPECIFIED UNSPECIFIED UNSPECIFIED Hayashi, Masahito UNSPECIFIED UNSPECIFIED UNSPECIFIED Chen, Lin UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-195475
DOI:	10.1103/PhysRevA.97.022342
Journal or Publication Title:	Phys. Rev. A
Volume:	97
Number:	2
Date:	2018
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	2469-9934
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ENTANGLEMENT MEASURES; QUANTUM COMPUTATION; POWER Multiple languages Optics; Physics, Atomic, Molecular & Chemical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/19547