A class of genuinely high-dimensionally entangled states with a positive partial transpose

Abstract

Entangled states with a positive partial transpose (so-called PPT states) are central to many interesting problems in quantum theory. On one hand, they are considered to be weakly entangled, since no pure state entanglement can be distilled from them. On the other hand, it has been shown recently that some of these PPT states exhibit genuinely high-dimensional entanglement, i.e. they have a high Schmidt number. Here we investigate $d\times d$ dimensional PPT states for $d\ge 4$ discussed recently by Sindici and Piani, and by generalizing their methods to the calculation of Schmidt numbers we show that a linear $d/2$ scaling of its Schmidt number in the local dimension $d$ can be attained.

8 pages

References in corpus (10)

• Entanglement detection
• Quantum Communication With Zero-Capacity Channels
• Optimal entanglement criterion for mixed quantum states
• Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
• All entangled states are useful for channel discrimination
• Steering bound entangled states: A counterexample to the stronger Peres conjecture
• Experimental bound entanglement in a four-photon state
• Class of PPT bound entangled states associated to almost any set of pure entangled states
• How often is a random quantum state k-entangled?
• Quantitative bound entanglement in two-qutrit states

Cited by in corpus (3)

• Dicke subsystems are entangled
• Entanglement in the Dicke subspace
• Rank-based entanglement detection for bound entangled states