Interconversion between block coherence and multipartite entanglement in many-body systems

TL;DR

This paper explores the quantitative relationship and interconversion between block coherence and multipartite entanglement in many-body quantum systems, demonstrating resource transfer and restoration under various operational constraints.

Contribution

It establishes the first set of quantitative relations for converting block coherence into multipartite entanglement and demonstrates resource interconversion under practical quantum operation limitations.

Findings

Multipartite entanglement is upper bounded by initial block coherence.

Multipartite entanglement can be transferred and restored via local operations.

Lossless resource interconversion is possible with coarse-grained operations.

Abstract

Coherence is intrinsically related to projective measurement. When the fixed projective measurement involves higher-rank projectors, the coherence resource is referred to as block coherence, which comes from the superposition of orthogonal subspaces. Here, we establish a set of quantitative relations for the interconversion between block coherence and multipartite entanglement under the framework of the block-incoherent operations. It is found that the converted multipartite entanglement is upper bounded by the initial block coherence of single-party system. Moreover, the generated multipartite entanglement can be transferred to its subsystems and restored to block coherence of the initial single-party system by means of local block-incoherent operations and classical communication. In addition, when only the coarse-grained quantum operations are accessible for the ancillary subsystems, we further demonstrate that a lossless resource interconversion is still realizable, and give a concrete example in three four-level systems. Our results provide a versatile approach to utilize different quantum resources in a cyclic fashion.