Bound entanglement in symmetric random induced states

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.

10 pages, 9 figures

References in corpus (32)

• Quantum entanglement
• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Entanglement detection
• Separability criterion and inseparable mixed states with positive partial transposition
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Unextendible Product Bases and Bound Entanglement
• Bound entanglement can be activated
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Generating random density matrices
• Low dimensional bound entanglement with one-way distillable cryptographic key
• Quantum states with a positive partial transpose are useful for metrology
• Bound entanglement provides convertibility of pure entangled states
• Class of PPT bound entangled states associated to almost any set of pure entangled states
• Four-qubit entangled symmetric states with positive partial transpositions
• Entanglement thresholds for random induced states
• Three-by-three bound entanglement with general unextendible product bases
• A (5,5) and (6,6) PPT edge state
• Family of bound entangled states on the boundary of Peres set
• Non-full rank bound entangled states satisfying the range criterion
• Searching for extremal PPT entangled states
• Entanglement and the truncated moment problem
• Construction of noisy bound entangled states and the range criterion
• A simple class of bound entangled states based on the properties of the antisymmetric subspace
• Bound entangled singlet-like states for quantum metrology
• Nonlocal Activation of Bound Entanglement via Local Quantum Zeno Dynamics
• Unextendible product bases, bound entangled states, and the range criterion
• Bound entangled states with extremal properties
• Is bound entanglement Lorentz invariant?
• Bound entangled Bell diagonal states of unequal local dimensions, and their witnesses
• Nonequivalence between absolute separability and positive partial transposition in the symmetric subspace
• Construction of Bound Entangled States Based on Permutation Operators