Bound entanglement in symmetric random induced states

TL;DR

This paper explores the natural emergence of bound entanglement in symmetric random induced states, demonstrating high-probability generation methods and analyzing their differences.

Contribution

It introduces two methods for generating PPT bound entangled states in symmetric multiqubit systems and compares their effectiveness and characteristics.

Findings

Bound entanglement appears with high probability for N > 3 qubits.

Two different methods produce distinct varieties of PPT bound entangled states.

The methods enable generation of large families of bound entangled states without complex optimization.

Abstract

Bound entanglement, a weak -- yet resourceful -- form of quantum entanglement, remains notoriously hard to detect and construct. We address this in this paper by leveraging symmetric random induced states, where positive partial transpose (PPT) bound entanglement arises naturally under partial tracing when proper parameters are selected. We investigate the probability of finding PPT bound entanglement in symmetric random induced states constructed via two methods: partial tracing of symmetric multiqubit pure states on the one hand (MI) and tracing out a qudit ancilla on the other hand (MII). For $N > 3$ qubits, we demonstrate that bound entanglement naturally emerges under optimal parameters, with a probability of occurrence very close to 1. We show that the two methods produce different varieties of PPT bound entangled states, and identify the contexts in which each method offers distinct advantages. These methods provide a versatile toolkit for the generation of large families of random PPT bound entangled states without complex numerical optimization.