Classes ofn-copy undistillable quantum states with negative partial transposition

Abstract

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

Quantum key distribution over noisy channels

“…In general, one might run distilled procedures in entanglement-based protocols. However, distilled procedures often with a large consumption of states while no all states can be distilled [33][34] [35][36] [37][38] [39][40] [41]. Hence, we argue how entanglement-based QKD protocols can resist certain noises, including CP, CR, Pauli noises, AD, PD and mixtures of them, without using distillations of entanglements.…”

A Few Steps More Towards NPT Bound Entanglement

“…In particular the authors have singled out a set of the Werner states which is expected to contain only non-distillable states. Moreover for any n they have shown a subset of the Werner states containing solely n-copy non-distillable states (see also [30] in this context). However the subsets are decreasing when n increases.…”

Detection of Tripartite Genuine Entanglement by Two Bipartite Entangled States

“…[ 31,32 ] To solve theproblem, there are several attempts by converting states into Werner states by LOCC. [ 33–35 ] Furthermore, progress toward distilling entangled states of given dimensions or deficient ranks has been made steadily. For example, Ref.…”