Abstract
We provide a simple construction of bipartite entangled states that are positive under partial transposition, and hence undistillable. The construction makes use of the properties of the projectors onto the symmetric and antisymmetric subspaces of the Hilbert space of two identical systems. The resulting states can be considered as generalizations of the celebrated Werner states.
Highlights
We provide a simple construction of bipartite entangled states that are positive under partial transposition, and undistillable
By considering the physically motivated framework of distant laboratories, where only transformations implemented by local operations and classical communication (LOCC) are allowed, entanglement is elevated to the status of resource
We know that noisy entangled states that are positive under partial transposition (PPT) cannot be distilled [4], and are called bound entangled [5]
Summary
We know that noisy entangled states that are positive under partial transposition (PPT) cannot be distilled [4], and are called bound entangled [5]. To focus on such a noisy kind of entanglement is useful and interesting for several reasons. One consequence of this is that, when discussing how noise affects tasks and tests that involve entanglement, the analysis of the role of noise is often less comprehensive than it could be This is because it is customary to focus on exemplary classes of noisy entangled states with a simple structure, like Werner states [17] (see Section III A) or isotropic states [18], which do not exhibit PPT entanglement in any range of the parameter involved. From their expressions (3) and (4), it is immediate to derive the following relations for normalized single-system state vectors |α and |β : PS |α
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
