Operational Entanglement Detection Based on $\Lambda$-Moments

Abstract

We introduce $\Lambda$-moments with respect to any positive map $\Lambda$. We show that these $\Lambda$-moments can effectively characterize the entanglement of unknown quantum states without theirs prior reconstructions. Based on $\Lambda$-moments necessary and sufficient separability criteria, as well as necessary optimized criteria are presented, which include the ones in [\href{https://link.aps.org/doi/10.1103/PhysRevLett.127.060504}{Phys. Rev. Lett. \textbf{127}, 060504 (2021)}] as special cases. Detailed example is given to show that our criteria can detect bound entanglement that can not be identified by positive partial transpose criterion, with the explicit measurement operators to experimentally measure the corresponding $\Lambda$-moments.

arXiv comment6 pages, 1 figure

References in corpus (21)

• Quantum entanglement
• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Quantum secret sharing
• Area laws for the entanglement entropy - a review
• Entanglement detection
• Entanglement negativity in quantum field theory
• Bound entanglement can be activated
• Quantum Clock Synchronization Based on Shared Prior Entanglement
• Further results on the cross norm criterion for separability
• Mixed-state entanglement from local randomized measurements
• Optimal entanglement criterion for mixed quantum states
• Optimal Entanglement Certification from Moments of the Partial Transpose
• Noiseless Quantum Circuits for the Peres Separability Criterion
• Universal quantum interfaces
• A characterization of positive linear maps and criteria of entanglement for quantum states
• Geometry of quantum states: new construction of positive maps
• Positive finite rank elementary operators and characterizing entanglement of states
• A class of 2^N x 2^N bound entangled states revealed by non-decomposable maps
• General construction of noiseless networks detecting entanglement with help of linear maps
• Mean of continuous variables observable {\it via} measurement on single qubit

Cited by in corpus (8)

• Entanglement detection in arbitrary dimensional bipartite quantum systems through partial realigned moments
• Higher-dimensional entanglement detection and quantum channel characterization using moments of generalized positive maps
• Visualization of all two-qubit states via partial-transpose-moments
• Detecting genuine multipartite entanglement using moments of positive maps
• Detection of entanglement via moments of positive maps
• A unifying separability criterion based on extended correlation tensor
• Efficient detection for quantum states containing fewer than $k$ unentangled particles in multipartite quantum systems
• Entanglement certification from moments of positive maps