Measurement-based local quantum filters and their ability to transform quantum entanglement

TL;DR

This paper introduces local quantum filters as a method to transform bound entangled states into detectable ones, enabling better entanglement detection through measurement-based implementations in small quantum systems.

Contribution

It presents a novel approach using local filters to detect bound entangled states that are otherwise undetectable by positive map witnesses, with explicit measurement schemes for qubit and qutrit systems.

Findings

Bound entangled states can be transformed into detectable states via local filters.

Explicit measurement-based implementations are provided for 2x2 and 3x3 systems.

The method enhances entanglement detection capabilities in quantum information processing.

Abstract

We introduce local filters as a means to detect the entanglement of bound entangled states which do not yield to detection by witnesses based on positive (P) maps which are not completely positive (CP). We demonstrate how such non-detectable bound entangled states can be locally filtered into detectable bound entangled states. Specifically, we show that a bound entangled state in the orthogonal complement of the unextendible product bases (UPB), can be locally filtered into a another bound entangled state that is detectable by the Choi map. We reinterpret these filters as local measurements on locally extended Hilbert spaces. We give explicit constructions of a measurement-based implementation of these filters for $2 \otimes 2$ and $3 \otimes 3$ systems. This provides us with a physical mechanism to implement such local filters.