New Classes of N-copy Undistillable Quantum States with Negative Partial Transposition

The discovery of entangled quantum states from which one cannot distill pure entanglement constitutes a fundamental recent advance in the field of quantum information. Such bipartite bound-entangled (BE) quantum states could fall into two distinct categories: (1) Inseparable states with positive partial transposition (PPT), and (2) States with negative partial transposition (NPT). While the existence of PPT BE states has been confirmed, only one class of conjectured NPT BE states has been discovered so far. We provide explicit constructions of a variety of multi-copy undistillable NPT states, and conjecture that they constitute families of NPT BE states. For example, we show that for every pure state of Schmidt rank greater than or equal to three, one can construct n-copy undistillable NPT states, for any n ≥ 1. The abundance of such conjectured NPT BE states, we believe, considerably strengthens the notion that being NPT is only a necessary condition for a state to be distillable. In the past decade, the search for efficient tools to determine whether a given quantum state is entangled [1], and if so, whether it can be potentially used in quantum information processing protocols has led to several fundamental results about the nature of quantum entanglement [2, 3, 4, 5, 6]. Almost all quantum communication protocols, such as teleportation [7] and super-dense coding [8], require maximally entangled states that are shared among the spatially separated parties in conjunction with classical communication. However, entangled states are noisy in general, due to environment induced decoherence effects. Hence, in order for an entangled state to be useful, one should be able to extract maximally entangled states (in the asymptotic sense) starting from an ensemble of the given state, while using only local operations and classical communication (LOCC). States which allow such extraction of maximally entangled states are referred to as distillable quantum states. Generalizations of classical information theory concepts have led to protocols for distillation of quantum entanglement from certain classes of quantum states [9, 10, 11, 12]. Recent results have shown that even though most entangled states are distillable, some are not. The undistillable but entangled quantum states are said to possess bound entanglement [5, 13, 14, 15]. Bound entangled states cannot be prepared locally as they are entangled Present address: Department of Chemistry, 80 Saint George Street, University of Toronto, Toronto, ON M5S 3H6, Canada Email: [email protected] Email: [email protected]