Higher-dimensional entanglement detection and quantum channel characterization using moments of generalized positive maps

TL;DR

This paper introduces a moment-based criterion for detecting higher-dimensional entanglement and characterizing quantum channels, enabling efficient experimental implementation without full state tomography.

Contribution

It presents a novel method using moments of generalized positive maps to detect complex entanglement and analyze quantum channels, advancing quantum information processing capabilities.

Findings

Effective detection of higher-dimensional entanglement demonstrated

Identification of non-Schmidt-number breaking channels achieved

Operational implications in channel discrimination shown

Abstract

Higher-dimensional entanglement is a valuable resource for several quantum information processing tasks, and is often characterized by the Schmidt number and specific classes of entangled states beyond qubit-qubit and qubit-qutrit systems. We propose a criterion to detect higher-dimensional entanglement, focusing on determining the Schmidt number of quantum states and identifying significant classes of positive partial transposition and negative partial transposition entangled states. Our approach relies on evaluating moments of generalized positive maps which can be efficiently simulated in real experiments without the requirement of full-state tomography. We demonstrate the effectiveness of our detection scheme through various illustrative examples. As a direct application, we explore the implications of our moment-based detection schemes in identifying useful quantum channels such as non-Schmidt-number breaking channels and non-entanglement breaking channels. Finally, we present an operational implication of our proposed moment criterion through its manifestation in channel discrimination tasks.