Quantum broadcasting of 3 ⊗ 3 negative partial transpose entangled states

Abstract

The utilization of quantum mechanical characteristics such as entanglement serves as a critical foundation in a multitude of quantum information processing tasks. With the objective of designing quantum networks, broadcasting - which is defined as the process of producing more quantum mechanical resources from a limited amount - presents an encouraging approach. One promising method of achieving broadcasting in quantum mechanical systems is through cloning operations. This thesis delves into the investigation of broadcasting of a class of quantum entangled states that go beyond 2 ⊗ 2 systems. It is known that beyond 2⊗2 and 2⊗3 dimensional quantum systems, Peres-Horodecki criterion is no longer sufficient to detect separability of quantum states. This is because there exists entangled states with both positive and negative partial transpose (PPT and NPT). Further, it is also true that all PPT entangled states are bound entangled states. However, in the class of NPT states, there can exist bound entangled states as well as free entangled states. All free/useful/distillable entanglement is a part of the class of NPT entangled states. In this thesis, the question is asked that given an NPT entangled state in 3 ⊗ 3 dimensional system as a resource, how much entanglement can we broadcast so that resource still remains NPT. The initial chapter offers a brief overview of the historical occurrences surrounding the evolution of Quantum mechanics. It is followed by a brief and succinct introduction to the necessary theory and mathematical tools required for this thesis. In the next chapter a 3 ⊗ 3 system is chosen as a first step to understand broadcasting of NPT states in higher dimensional systems. In particular, we find out the range of broadcasting of NPT entanglement for Two parameter Class of States (TPCS) and Isotropic States (IS). Interestingly, as a derivative of this process we are also able to locate the existence of absolute PPT states (ABPPT) in 3⊗3 dimensional system. Here we implement the strategy of broadcasting through approximate cloning operations