Multipartite Entanglement Structure Resolution Analyzer Based on Quantum‐Control‐Assisted Multipartite Uncertainty Relation

Abstract

By constructing a quantum-control-assisted multipartite uncertainty relation, a general and efficient multipartite entanglement structure resolution analyzer is provided for all pure states with arbitrary number of parties in arbitrary finite dimension. The lower bounds of this multipartite uncertainty relation present different spectra for different multipartite entanglement structures, and they thus can be considered as a form of resolution analyzer for the multipartite entanglement structure. The resolution analyzer obtained delineates the detailed structure of multipartite entanglement with a suitable number of incompatible measurements, without a complete prior knowledge of the quantum state.

Dynamics investigation of the quantum-control-assisted multipartite uncertainty relation in heisenberg model with dzyaloshinski-moriya interaction

“…x z q = 0.5. conditional uncertainty relations, one can in fact obtain that the single-valued relationship between the mixedness and conditional uncertainty relation does not rely on the form of the uncertainty relation. The conditional uncertainty relation reduces the uncertainty of measurement results mainly by the quantum correlation between the memory system (or control system) and measured system, and conditional uncertainty relation thus has an inevitable relationship with the quantum correlation [19,24]. Also, some works indicate that, the mixedness has a close relationship with the quantum correlation [33].…”

“…1 have been performed [24]. The construction of the QC-VUR successfully extends the conditional uncertainty relation to the multipartite case, and promotes the development of uncertainty relation.…”

“…In fact, QM-EUR is essentially a conditional uncertainty relation based on entropy [19], and its construction opens up a new direction for the understanding of uncertainty relation [20][21][22][23]. However, due to the complexity of conditional entropy, the investigation of the conditional uncertainty relation develops slowly [24].…”

“…To fix this problem, Zheng et al recently constructed a conditional uncertainty relation in form of variance, which is named as quantum control-assisted variance uncertainty relation (QC-VUR), and showed that the traditional variance uncertainty relation can be broken with the quantum control systems [24]. The obtained uncertainty relation can be illustrated by the following game: 1.…”

“…Therefore, the measurements implemented on the corresponding control systems are called quantum control. QC-VUR is essentially a conditional uncertainty relation, and can be expressed by the following inequality [24]:…”