Complementarity in Quantum Information Processing Tasks

TL;DR

This paper introduces new complementary relations in quantum information processing, analyzing how broadcasting entanglement affects the usefulness of resulting states in tasks like teleportation and superdense coding, using both local and nonlocal cloning methods.

Contribution

It establishes bounds on the capabilities of less entangled states created via broadcasting, extending to different cloning transformations and resource states.

Findings

Boundaries of teleportation fidelity with broadcasted states

Limits of superdense coding capacity after broadcasting

Effect of different cloning methods on entanglement quality

Abstract

Complementarity have been an intriguing feature of physical systems for a long time. In this work we establish a new kind of complimentary relations in the frame work of quantum information processing tasks. In broadcasting of entanglement we create many pairs of less entangled states from a given entangled state both by local and non local cloning operations. These entangled states can be used in various information processing tasks like teleportation and superdense coding. Since these states are less entangled states it is quite intuitive that these states are not going to be as powerful resource as the initial states. In this work we study the usefulness of these states in tasks like teleportation and super dense coding. More precisely, we found out bounds of their capabilities in terms of several complimentary relations involving fidelity of broadcasting. In principle we have considered general mixed as a resource also separately providing different examples like a) Werner like states, b) Bell diagonal states. Here we have used both local and non local cloning operations as means of broadcasting. In the later part of our work, we extend this result by obtaining bounds in form of complimentary relations in a situation where we have used $1-N$ cloning transformations instead of $1-2$ cloning transformations.